The Prologue of Baldur's Gate 3 takes place immediately after the opening cinematic, in which the main character is infected with a Mind Flayer larva. The Nautiloid in which this takes place is attacked by Githyanki warriors, allowing the main character to break free. While trying to escape the attacking Githyanki, the mind flayer controlling the ship warps it into different planes of existence, ending up in Avernus, the first of the Nine Hells. The objective of the Prologue is to find a way out of the Nautiloid, ideally not by dropping down into Hell.
Walkthrough
Nursery room
This is the room in which the game begins. The main character has broken free out of a Mind Flayer Pod and is standing alone in the room. Around the room there are various empty mind flayer pods indicating that there might be other survivors.
In the middle of the room there is a mind flayer "nursery" i.e. a pool filled with larvae. Upon interacting with it, you can Investigate it to determine that it's about to break apart. If you try to touch it, it explodes and causes a small amount of damage to your character.
To the south of the nursery you can find a dead mind flayer. Looting him yields a Spiked Bulb.
Further south you can climb up to a small elevation in the room, where a dead Mind Flayer Thrall can be looted for a Scroll of Mage Armour and 3gp. Lying aside him is a Slave Mind --a human brain preserved in a jar-- that can be picked up.
To the east of the room, slightly southward, you can go up to a larger elevated area of the room, circling around it all the way to the northwest. Along this elevated area you can find: 1. a Cartilaginous Chest containing a Potion of Healing and a Potion of Fire Resistance, 2. a Caustic Bulb lying on a table, and 3. a second Cartilaginous Chest containing a bottle of Alchemist's Fire and a Grease Bottle.
On the west side of the room you will find an illithid restoration device that fully heals you upon interaction, and a door to the next room.
Brain room
The dead bodies of three Lesser Imps will greet you in this room. Loot them for a Potion of Healing and a Scroll of Fire Bolt. Directly aside their bodies is a table on which you can find a Caustic Bulb, three Mucoid Shells, a Sodalite Shell, and a Barbed Device. These are mostly junk items; only the bulb has a use.
Back near the entrance, there's another table with an Illithid Record and a Hollow Shell. The shell is a junk item, but the record can be interacted with to reveal that it contains knowledge about Goblin culture.
Further westwards and to the north of the room there is a table on which you can find an Eldritch Tablet, an Illithid Manuscript, and a Dark Mind (another brain in a jar). The tablet and manuscript can be interacted with just like the illithid record. The tablet contains knowledge about humanoid history (elves, dwarves, humans, etc.), and the manuscript seems to tell a story about "a brain, a githyanki warrior, and centuries of darkness."
In the middle of the room, a small elevator can get you to an upper section of the room. Here you will find a dying person sitting on a chair with their scalp removed, their exposed brain telepathically asking you for help. Otherwise, you can find here a pair of Cartilaginous Chests containing random loot.
When you interact with the person in the chair, your character may be able to notice that the exposed brain is not in fact the person's own brain, but rather an Intellect Devourer. You have various options to try to free the creature from the skull, although you can also just leave it in place or destroy it outright. Should you choose to free it and succeed, it can give you a bit of information about your situation, and will become a temporary companion who can assist you in battle.
While freeing the Intellect Devourer from the skull, you also have the option of trying to mutilate it to make it more obedient to you, although this seems to be unnecessary as it's obedient to you either way, and failing the ability check while trying to mutilate it will cause the creature to go hostile.
To the west of the room there's an opening in the Nautiloid's shell. An outer path leads northwest, where you have to jump over a gap and will have your first encounter with the Githyanki soldier Lae'zel, who was previously seen in the opening cinematic, also being infected with a larva.
Imp battle room
As Lae'zel jumps down from a ledge to attack you, the telepathic connection between you caused by the mind flayer larva makes her realize that you're not under mind control, and that the two of you could cooperate. She insists that you go to the helm of the Nautiloid, where you can take control of it.
In the room ahead that you need to pass, there are three lesser imps that you need to defeat. This is most easily done with ranged sneak attacks. One imp will drop a Handaxe and another a Light Crossbow. Other than that, you can loot a dead mind flayer in this room for two void bulbs and a potion of healing, and another dead mind flayer who has been incinerated can be looted for a Potion of Speed, a void bulb, and a caustic bulb.
You can exit this room to the west, climbing some stairs out to open air and towards the nose of the Nautiloid. There's a healing pod too before the stairs, should you need it.
Nose of the Nautiloid
A short cinematic will play as you walk out into open air, in which the nose of the Nautiloid in front of you is badly damaged by attacking red dragons. Thankfully this doesn't affect our route.
Various dead lesser imps and thralls can be looted here for minor riches and equipment, including a Studded Shield. One incinerated dead thrall all the way towards the nose of the ship has a Potion of Poison Resistance. You just have to jump over some fire to reach the body. She also holds on to yet another brain in a jar, and this one is called Our Mind.
Turning back, you can climb another set of stairs to reach an upper level of the Nautiloid. Here, an Intellect Devourer will tell you that you must go to the helm of the ship to provide assistance. You can choose to attack, but the ensuing fight may actually prove difficult as there are also two lively thralls here maintaining some cannons. If you want to kill them for the little XP you will get, ranged sneak attacks might be the best option.
There are also two lesser imps towards the south here having some sort of argument, one of them already wounded. Just use some ranged attacks on them and you can easily finish them off.
Talking to some of the dying Enthralled Cultists on the ground around this area can give you a little insight on how they think. One will talk about red, flying rats in the kitchen clawing at him, clearly referring to the imps who attack the thralls. Another will speak as if he's talking to his mother, saying that he's tired and wants to go to sleep early. Although talking to them reveals, rather tragically, that the thralls are just poor, regular humans under mind control, you can nevertheless finish them off for some very minor gold and XP. (They are about to die anyway, might as well put them to rest.)
The path forward is back into the Nautiloid via a corridor to the north, stretching east. There's a mucous membrane you just need to attack to break through, and then a door leading into the next major room.
Shadowheart room
In this room you will be greeted by a pair of knocked out cultists on chairs, and some sort of control panel with three pairs of sigils and buttons. Lae'zel will warn you not to touch anything.
You will also hear a woman trapped in a mind flayer pod thudding against its glass encasing. It's Shadowheart, who will suggest you try to use the contraption next to the pod to get it opened. Looking at said contraption will reveal that there is an empty socket of some sort. You need an object to fit in there.
Aside Shadowheart's pod, there is a backpack with some minor riches in it like some gold and an Agate. To the south, there's a table with various objects on it: a Burnished Necklace, a Scoll of Inflict Wounds, a Scroll of False Life, and a locked Elaborate Reliquary. You might be able to pick the lock of the reliquary, otherwise you can look for the key. It will contain 15gp, an Onyx, and an Eldritch Rune that can be inserted into the control panel of Shadowheart's pod to free her.
If you have Lae'zel as a companion, Shadowheart will be a little snarky, but either way she asks to join you as a companion.
You might notice that an Intellect Devourer occasionally walks through this room. You can kill it easily if you surprise it, but it won't drop anything. The two cultists in the chairs can be interacted with and will seem awake, but totally unresponsive.
Going back towards the entrance, you can look at the sigils on the control panel. Each will trigger an Arcana check to allow you to read it. The left one says "Unleash," the middle one "Aggression," and the right one "Annihilate." The Unleash button apparently makes psionic energy radiate from the two knocked out cultists, but it's unclear what use this has. (It does not allow you to talk to them. This might be just unimplemented yet.) The Aggression button will make them attack you, and Annihilate will, unsurprisingly, kill them. Making them attack you and then defeating them gives you 1 XP each if you're into that. Looting them can also be done by just pressing Annihilate. They hold 3gp in total, a Quill, and a Small Bottle; in other words, junk.
If you weren't able to pick the reliquary containing the Eldritch Rune for Shadowheart's pod, you'll want to look into the room to the east to find the key. To the south, in turn, you can finally enter the helm.
Ceremorphosis room
In this room there's yet another mind flayer pod at the center. This one contains a dazed woman who seems unresponsive. Behind her is a console with a sigil and a button. The sigil yet again triggers an arcana check, and succeeding it reveals that it says "Perfect." Gee, what could that mean in mind flayer logic? Pushing it makes the woman in the pod become a mind flayer.
On a raised platform at the back of the room there's a dead thrall on which you can find the key to the reliquary in the previous room.
There's nowhere to go from this room but back to the previous, so at this point you can go back and south, towards the helm.
Helm of the Nautiloid
As you enter the helm, you will see a mind flayer fighting Commander Zhalk, a powerful Cambion wielding a flaming greatsword. A cutscene will play in which the mind flayer orders you to connect the nerves of the transponder, referring to the control apparatus of the ship that allows it to travel between dimensions. The flayer thinks that you're a thrall, thus considers you an ally.
A pair of lesser imps and a Lesser Hellboar will block your path, but they should be easy to defeat if you have both Lae'zel and Shadowheart as companions. One of the imps carries a light crossbow, the other a Scimitar.
There are also lots of dead bodies on the floor, though none contain any notable loot. A dead thrall can be looted for a Leather Armour and a Short Sword, an already-dead lesser imp for yet another light crossbow, and two more thralls for further short swords.
You can find two more Caustic Bulbs in this room as well, lying on tables (one in an upper area of the room), but it's probably not worth chasing after them.
While all the cutscenes and dialogue in this scene of the game tell you to ignore Commander Zhalk and reach the console, it's actually possible to help the mind flayer kill him. This gives you a large XP boost, and he will drop the greatsword Everburn Blade.
Don't take too long though, as a pair of Cambion soldiers will enter the room to join the fight at some point. They are almost as powerful as Commander Zhalk himself, so if they defeat the mind flayer and start attacking you, the battle will become nigh impossible. Although killing them might give you another big XP boost, this is almost certainly not worth the effort. (By killing Zhalk, you're already gaining more XP from this section of the game than you're really meant to.)
Nearing the console also makes another two lesser imps and another lesser hellboar appear, though again these should be easy to kill. Once you've reached the console, interact with it to start a cutscene and end the prologue.
The crash (cutscene)
In the cutscene that follows, the character that interacted with the neural console will connect two arms to make the ship warp out of Avernus and back into the Prime Material Plane, but moments before the warp a red dragon latches on to the ship and breathes fire onto the console.
As the ship appears in the sky of the Material Plane, a Tiefling behind a telescope is seen looking at it with worry, and in another place, a Hobgoblin and a Drow (later revealed to be Minthara) look at the ship with satisfaction, though they are slightly worried as an explosion erupts at the backside of the ship, accelerating its burning. They order a group of goblins to march out of some sort of fort they seem to be occupying.
Back in the crashing Nautiloid, our main character is trying to hold on, but is hit in the face by a piece of debris and sent flying out of the Nautiloid. As the character falls to the ground, moments before impact they are held mid-air by magical force and end up having a soft landing. There's nobody nearby, indicating that this might be the doing of the mind flayer larva lodged behind the character's eye.