Outside of combat use them:
On landing in combination with throttle
Taking off with heavy loads (bombers, attack fighters from carriers) or short runways (carriers for certain aircraft)
Any time you want to reduce stall speed
During combat use them:
To help you over the top of a loop at stall speeds
To tighten the corner on your opponent
General information:
Aircraft have differing flap speeds. For instance, most U.S. aircraft deploy at 250 mph, German at 175 and British at 150 although there are exceptions. I use these examples as they're most familiar to me.
Aircraft have differing flap settings. For instance most U.S. aircraft have five deployed settings, German three and British three with the major exception being the Spitfire at one (down).
In some aircraft, flaps are incredibly helpful. In others they're a hindrance.
In some aircraft or in certain situations, the use of other controls such as rudder or throttle (including WEP) can make flaps usage more effective.
The general consensus is to use just enough flaps (both in level of deployment and in time of deployment) needed to accomplish your goal. That said, you'll find "full flaps" fights in your time in AH.
Hope that helps.