The hint button is your friend. Once used, it will only be accessible again after you've tried a few new item combinations.
Press the crosshairs button to highlight all the interactive hotspots in the current room. Invaluable, as some important items are almost invisible.
It's a (particularly obtuse) point-and-click game, so talk to everyone, try to pick up everything, and if in doubt, use every item on every other item.