strains are created by inbreeding, just like any other "breed" of animal. Its generally referred to as line breeding and is a specific technique of inbreeding. Properly done it works OK, but its not quite as easy as it seems. A pool or group that is inbreeding will eventually fail if you never introduce new genetic material. That is a fish, usually with traits similar to the ones you are after but is not related to your fish, which is called outcrossing.
Inbreeding does not happen instantly and depends a lot on genetics. Usually with a healthy parent generation with fish that are from very different souses you can go awhile if your do it correctly, before you need to outcross. If both parent fish though are carriers of a genetic mutation it will show up very quickly in offspring. Eventually if inbreeding continues offspring will all become very very similar to each other. Diversity though is they key to any species success. If they are all so similar they have the same weaknesses. So genetic diseases show up, or a actual disease will come an wipe them all out.
Its the same with like pure bred dogs for example. Each breed is the result of line breeding. Many breeds are prone to common genetic diseases, some have very short life spans. Often though you can find breeders who have done careful breeding to guarantee against a certain genetic disease. Aquarium fish strains, especially livebearers are line bred. Same with any other "breed" of cat, horse, cow, chicken, ect... A lot of the things that make a breed are mutations, weiner dog is long, guppy may be solidly black, balloon fish is short, cow is black an white. <They are all mutations from the original species. Mutations can happen anywhere in the DNA. While some not at all harmful, some are deadly, other are controversial. Some are right on the line, Scottish fold cats can have folded ears or normal ears. No ethical breeder though would breed two cats that showed folded ears, because it is very likely the offspring will have a sever mutation in cartilage and bone structure.
Too keep a strains pure with fish, most breeders cull the offspring. How much varies depending on the breeder. Basically you pick a group of offspring that show the best traits you are after and remove the rest from the line. Then you just use those offspring and the parents to continue the line.