Adventure game veterans probably know these things already, but if you are new to the adventure genre, here are some general tips:
1. Pick up anything that's not nailed down.
2. Talk to everyone.
3. Try to use the items in your inventory with each other and objects in the environment.
4. If you're stuck, try to talk to other characters again. They might have a new topic to talk about.
If you have any more suggestions for tips, please post them and I'll add them to this list.