Since the Slayer Quest is an optional subquest, you can do it whenever you like, not necessarily before meeting the Necromancer the first time. This quest is dangerous, although not very long, and you might feel that it is better to do it when you are better equipped.
However, by getting the Slayer mace early in the game you have the advantage of having a very powerful weapon early in the game.
Whenever you feel like entering the Slayer subquest, go to the east road and find a small wooden building somewhere to the east with a stone amber in the middle. When you walk near it, the ground will give way beneath your feet and drop you in a new area.
Something that few know is that the dungeon in which you find the Slayer is actually Treasure Cove. Treasure Cove was thought to be one of those places that were omitted from the game, but Kobra Kai proved the contrary sending me a screenshot on 29th July 2003. I checked it out myself and took another screenshot:
If you need to refer to a map, you can see the map of the Slayer Quest on Pentology: Ultima VIII Cluebook hosted by Kravlor Dragon. If you want to read the books in the Slayer Quest online, consult the writings I collected.
After having fallen into a new area, there is no way back except either recalling out or finishing the quest.
You will be in a room with a troll running after you. Get the key at the uppermost corner from among the bodies (shown clearly in this picture). It opens the trapped chest (which contains a key) and the door. You should also read the book before leaving the room, as it tells you about the Slayer, and directs you to find the next book.
Go southwest and west to a building. Climb up and read the book.
Jump back down and go west, then turn south and follow the path till the next intersection, which will have spiders and cobwebs. Go south through the webs and continue to a door inside which are peasants and a troll. Take the key from the backpack at the west end of the room.
Go back to the last intersection and back to the first. From the first intersection, go north and follow the path north, and east when it turns east, going around the rocks to proceed in that direction. You will eventually come to a turning south. Ignore it and continue east, as it is just an alternate way to get where you are (by going north from the second book and pulling the lever to lower the metal wall, in which a ghost would appear).
Keep going, past a seeker, to another book. You can read it if you want. There is nothing to the south, so go north, climb the short wall and jump onto the island. Climb the ledge and go down on the other side. Hop over the stepping stones to the next island. Go west, and you will find a fourth book in front of a door, and sometimes even a seeker. Unlock the door with the key you found in the room with the troll and peasants or, if you don't have the key, remove the book and climb onto the pedestal and into the building.
Either way, enter the large building and approach the doors. The skeletons will attack you, so you might want to run around the smaller building to evade them. Go into the smaller building either through the doors or by climbing over a wall, and climb over the door with the cobweb to get to the Slayer.
Take the Slayer and, when you want to leave, just enter the door with the cobweb. You will be taken to a wooden building in the northwest corner of East Road, and if you are doing everything in the order of this walkthrough and will visit the Cemetery next, the Cemetery entrance is just east of this building.
