Hi, concerning the wold quest of the prologue. I know that I have to either bash the door open, or pick the lock but I don't know how to do either of them.

I have a fighter/thief but the thieving skill is grayed-out no matter how close to the door I am. I can press the button and click on the door, but it keeps saying locked.

I have also a dwarf fighter who can bash doors (I guess) but I don't know how to do that.

Any help?

Check your thief's armour. He can't do thievery if wearing heavy armour. If lockpicking doesn't succeed his skill is probably too low.
IIRC you need to use the attack icon to bash doors