The problem with Aiptasia is that is the proverbial rabbit of the reef..it breeds and spreads like crazy.
There are a couple of methods to get rid of it but as davyboy pointed out no method is 100%.
1. Peppermint Shrimp: these guys will take care of the smaller Aiptasia but this is what I found out. There are two types of Aiptasia..a pacific version and an atlantic version. THe PAcific version is the stuff that spreads rapidly; the atlantic version isn't as aggressive. I had the atlantic version and while I got rid o 3 of them, I still have one that hasn't spread in over 5 months. Peppermint shrimp from the pacific will not recognize atlantic version Aiptasia as a food source and vice versa. In other words, unless you can definitively identify the area and related peppermint shrimp, you have a 50/50 shot of the Peppermints actually eating the Aiptasia. I had that. I had Aiptasia and went gleefully down to my LFS thinking..I'll fix you. The shrimp ignored the Aiptasia. I know I have Atlantic rock and related Aiptasia but obviously the Peppermints were the west coast variety.
2. A couple of chemical methods but it takes some detective work and point and shoot action.
The first is using a mixture called Aiptasia-X which is usually available at your LFS. I have never used this so can't give instructions but I imagine it is basically the same method as the one I am going to describe next
Another method is using a mixture of concentrated Kalkwasser. Mix 1 tablespoon of Kalk with 2 tablespoons of water. Mix. Turn off any waterflow..you want the water column as still as possible. Using a syringe, suck up the mixture and then carefully coat the Aiptasia and the hole it is going to retreat into. When the kalk hits the water you are going to see a snow like precipitation. Be careful not to get the mixture on other corals nearby as concentrated Kalk will kill just about anything. If you do get the Kalk on something else, just use your finger to gently stir the water in the area to clean it off. Leave your pumps off for about 15 minutes and then you can turn them back on. What little Kalk goes back into the water when the pumps come back on won't hurt the general tank as it is kept moving and can't really settle. The three Aiptasia I used this method with never came back. The one I still have is just in a bad location but as long as it remains a single, I will leave it be.