I know this is a super stupid question, but I've downloaded the game and unpacked it, and I don't know what to do to launch it. Do I do something in the terminal? Do I click a specific icon? I'm using the latest version of Ubuntu.
Nvm I found it. If anyone's wondering:

1) Open terminal
2) Navigate to the path where the game is unpacked
3) Type:
./start.sh

That is what you're supposed to do, however mine doesn't work either. I think we need to mark start.sh and maybe WL2 as executable first then look for dependencies.

They should already be executable.
Try to launch WL2 directly if start.sh doesn’t work.

"Doesn't work" isn't much help... if you're using a different distro than the "officially" supported ones (like me who uses Debian Sid for example) you might need to remove the libstdc++.so.6 from the game (in lib/) to use the system one.

But it might be something else, if you don't have give more details on what is your setup (what distro, 32/64 bits, what graphical driver stack, ...) and what exactly happens, it'll be hard to help.

Woups, forgot this part!
Here is the list of Wasteland 2 dependencies if you launch it directly from the WL2 binary:

While I don't need help myself, it's generally good procedure to post your findings so that any future searchers can find aid.