I was charge for a in-app purchase but didn't receive what I purchased.

FIrst, you contact the developer. THere should be contact info in their iTUnes profile (where you downloaded the game from. failing that you can google them and find their site)

If you can't get satisfaction from there then you contact iTunes and get them to help you http://www.apple.com/support/itunes/contact/

The necessary links/menus you need to navigate to after clicking the Report a Problem link can be a little tricky to find. See

Refunds from the App Store or iTunes Store