They're called point and click / Hidden-Object Puzzle Adventure / Roll Playing.
Sites with a lot of these types of games are: Bigfishgames.com and Toomkygames.com. I'd recommend you download and play a few to get an idea of what to do. (Bigfish you can play a demo free for 1 hour which is probably sufficient to give you a good idea ). Toomkygames gives you the full game for free.