Aiptasia are photosynthetic, and are right at home in well fed high nutrient environments. They reproduave by pedal laceration which means a piece of the foot rips off and becomes another one.
The best methods I've found are the ones which utilize some srt of biological control. If you have any number of them then human control just isnt enough.
Several critters eat them.
Copperband butterfly fish - These can be very difficult to keep in captivity, and I wouldnt recommend one until you become very familiar with them and are sure you can provide them with an adequate home.
Peppermint shrimp - There are several species that can be found at LFS, and not all eat aiptasia. You'll need to become familiar with how to identify the species, they are similar in appearance but distinguishable. These guys can also be a bit destructive mostly at feeding time if they dont recieve their fair share. They are fairly hardy and can survive without aiptasia by scavenging.
Berghia Nudibranch - This nudi feeds exclusively on aiptasia, and does a good job of it. Problem is they dont feed on anything else. They also will reproduce in your tank. Their population will rise as they eat the Aiptasia but as food supplies dwindle they will begin to die off. If more food doesnt become available they will die off completely usually leaving some aiptasia behind. Sources of these are few and they are expensive.