Berghia are hardy creatures but delicate at the same time. Their tiny cerata, the frilly edges of their tiny bodies, can be damaged by nets or scraping. I like to place them in a small cup, into the water where I want them to live, and let them climb out on their own. If you place them near each other, near an aiptasia, they will thrive. But, being nocturnal, chances are you will never see them again. You will notice the aiptasia disappearing after a while. It takes a bit, because the berghia will get the ones under the rocks, behind the rocks and hidden from view first.
Some wrasses, butterflyfish, filefish and some dottybacks will hunt for berghia. and their eggs. Not all, of course. I have all these types of fishes and have not seen this in my experience. But, predicting a particular fishes behavior is impossible. A well fed fish usually will not eat a nudibranch. So, for the first week or so, maybe feed a little extra? And, turn off any moonlights or nighttime lighting, when the berghias are out hunting.
Peppermint and coral banded shrimp are a serious threat to our little nudi, and also to our corals. Some aggressive crabs can be, too.
The cup your bergia arrives in can be floated in your tank for a few minutes to let the temperatures equalize. Check the salinity in the cup and your tank. Then, pour out approximately one fourth of the water in the cup, into a drain, and add some of the water from your tank. Depending on how different the salinity is, you may have to do this a few times until the salinities are the same. At that point, you can release the nudibranchs out of the cup. You can place a rock on the cup to keep it in one area while the nudibranchs climb out. They are slow, but once they smell their dinner, they can be amazingly quick!
Other interesting information
Your berghia are egg laying size, so if you see a ribbon of eggs, leave it alone. Amphopods may munch on it, but maybe not, because many aiptasia farms have been decimated by an unexpected egg on a turkey baster!
Some internet websites recommend at least 8 berghias for tanks over 100 gallons. They need to be able to find each other to reproduce. I have placed 4 per cup, ranging in size, but they are all capable of reproducing. For tanks 50 gallons or less, this should do the trick. Unless you want the issue fixed quicker! It seems healthy berghia can eat a medium aiptasia each day, so if you are patient, a few can do the trick.
Remember, the nudis are nocturnal, and they will eat the out of sight aiptasia first. It may seem like they are not doing any good for the first week or so, because they are eating the spores and tiny ones first. They save the largest ones for last, and gang up on them! If an aiptasia is bothering one of your favorite corals, give it a clip with some scissors. The bergia will take care of it the rest of the way.