Documentation
There is no proper user manual for WorldPainter (yet). I tried to make it as self-explanatory as possible, and you should be able to figure most of it out by trial and error. Click (left and right) every button and see what happens. Don't forget to try every mouse button, using the scroll wheel, and doing these things while pressing Ctrl. Also don't forget to look through all the menus.
Having said that, there is some documentation:
Mouse, tablet and keyboard controls.
Frequently Asked Questions / HOWTO
How to use the Populate layer
How to use the Caves/Tunnels layer
How to edit existing maps
How to use the Biomes Viewer
Developers
How to use the scripting engine
How to use WorldPainter in your own code
How to build WorldPainter locally
Credits
WorldPainter includes the work of many others. The Credits page lists them.