Most things are self-explanatory. I advise you to create a map for playing around with the tools, learning by doing.
Some basics that may be handy:
Layer counts and chunks get important when using more than 8 different tiles. If this is the case there must not be more than 8 tiles per chunk. If you add a ninth that tile would become blackend out. That's where the checkable box is very usefull. If you check a layer it will be blackend out and it's easy to find out where which layer was used.
There are two (not counting the possibility of deleting the whole tile) ways of erasing tiles: Use the erase button to get rid of a tile in a specific chunk or paint it over with another tile.
The third button is for merging layers, and this is one that I do not really understand. If I try to merge 3 layers, for example, afterwards 2 of them disappear, which is expected. But the remaining layer is one of the 3 that was already there (not sure how it picks which of the original set to keep) and the look of what was painted changed because the actual texture used in 2 our of the 3 layers is completely lost, replaced by the texture of the single remaining layer. Is that what is supposed to happen? So merging just merges the painted areas, but not the textures themselves?
Merging always merges tiles from top to bottom: The lowermost layer is always the the first layer on a map.
For example:
1. Grass 1
2. Grass 2
3. Soil 1
4. Sand 1
5. Grass 3 (base tile, cannot be deleted)
If you would merge layers 1, 2 and 4 everything would be converted into the 4th layer (Sand 1).
The next section is labeled "Burner" and I have no idea how to use it. I'm sure I'm missing something important here.
No you don't miss anything here. Ignore it. You won't need it.
The next section - "Textures" - is fairly self-explanatory except for the icons (red X, green checkmark, and a combo of both) which I do not yet fully "get". The state of each also changes depending on whether I've been working on the map in a single WorldBuilder session for a long time, or if I just reopened the application. But I don't think there's anything too critical I'm missing here - mostly just curiosity for the sake of completeness.
red x: Texture not in use
green checkmark: Texture in use
combo: bugged, will change to green checkmark when the clicking on the texture again after you used it.
The next (4th) button is apparently for adding layers. Sometimes this works, and sometimes it's greyed out and I can't add any more layers. This has happened when I just have 3 layers total, so I doubt it was hitting the limit (what is the limit on number of layers, by the way?). If I save, exit, restart and reload I can then add layers again, so there's no rhyme or reason to why it sometimes stops working. Bug?
Look's like a bug. Never had problems adding textures. Just tried it out and after a dozen I stopped adding.