(I will basically follow the player's guide's starting walkthrough for convenience.)
1. Entrance. Grab the bag for your map and some starting equipment.
2. Make sure to grab the bowl and the torch. The axe is optional, depends on your weapon preferences.
3. Grab ORT and JUX. You can't do anything with them yet, but that's ok.
4. Grab the backpack. Put all the runestones into the rune bag and put it somewhere convenient to access. Read the note and then drop it.
Here you get the RED KEY, which opens doors marked with A on my map.
You now have runes BIJLOS.
5. Pull the chain to get in. Grab the bag and unlock both doors.
6. Do the thing with the silver seed. Go to the east end of the room and search for secret doors. Head on through.
7. Easiest way to make these jumps is to get to the edge and use Shift-J, which is a standing forward jump, a fact the player card neglects to mention when it describes jumping.
Hit the button, go through the door. Read the walls to learn your first three mantras. Then I recommend saving and using SUMM RA until it gives you useful stuff.
Then jump to the remaining platform. Grab the GREY KEY [B] and unlock the door- now you can use this path to get back up if you fall into the water. (If you fall in the water first, you can break the lock with a single weapon blow.)
8. Look at the Orb. Remember what it shows you: the green path. Also, there is a rotworm to kill on the way in- grab its corpse and hold onto it for the rotworm stew later.
9. Bedroll. You'll want this.
Just outside this room is Bragit, an Outcast. He'll tell you some about this floor of the Abyss, and also offhandedly mention something that comes in useful in general- you can use a pole to push buttons beyond your reach. Note that you cannot do this with a fishing pole!
10. Switch that opens the door at the north end of the room.
11. Two poles and a box. You can grab the box for inventory space but ditch the sling and stones. One of the poles you'll turn into a fishing pole and solve all your food problems forever, the other you can keep to actually use as a pole.
12. Two Outcasts. They teach you some about the Abyss.
13. Gulik and Hagbard. Both are Outcasts; Hagbard is their leader.
14. Box with two runestones (M and Y). There's a Lurker in the water here, and they're pretty tough at low level, so you might want to grab the box and run.
You now have runes BIJLMOSY.
15. In here is another copy of key [B], and some stairs down.
16. A spellcasting monster lives in here but he isn't too tough. In here is a scroll that tells you how to cast a Jump spell (Uus Por).
17. In here is Drog, a green goblin guard. He's not very nice but he'll open the portcullis if you ask.
18. Talk to Lanugo, the guard first. You can bribe him with a single gold piece. He'll tell you to be very flattering to the king. Be polite and he will give you the recipe for Rotworm stew, which you will want later on. Keep the paper the recipe is on- unless most things in this game where the paper just teaches you how to do it, here you actually need to Use the recipe to make the stew.
19. These four dials control the heights of the four platforms in the room to the west. To get to the small chamber above the room, you want to make a zig-zag staircase of sorts. To do this you want to basically reverse the heights of the 4 moveable platforms. (The solution by dial is, from left to right and with 0 as straight up: 0 1 3 4.) The room's contents- a gravestone and a box with most of a suit of leather (which you should have by now), a worn axe (no better than what you probably have by now unless it's magic and I didn't realize), a "resilient sphere" which I don't yet know what they do, and a scepter of mana boost. (NOTE: Having finished the game, I found two resilient spheres and no sign that they have any use whatsoever.)
20. Eb the grey goblin guard.
21. Retichal. You need her permission to talk to the king. Then go through the door to the south and speak with Ketchaval, King of the Gray Goblins. He'll tell you about Navrey Night-Eyes. Probably best if you don't mention having spoken with the Green Goblins.
22. Navrey. It's a good idea to grab the leeches from the cave before the bridge, as Navrel poisons. Grab all three things of thread, and drag one onto one of the two poles to turn it into a fishing pole. Thus are your food problems solved. The other two will be valuable later.
23. Through a secret door is this fountain, which heals you.