As a small guide into buying healthy fish. Try and stick to aquatic stores as opposed to pet stores. I have nothing against pet stores. It's just that aquatic stores spend more time keeping their tanks clean. As well as knowing more about individual breeds.
When buying your chosen fish look out for a couple of things. First, make sure that the fish is alert. Any colours that it may have should be bright. All fins should be intact. Any fish that sulks away in a corner with dull colors and tattered fins may be ill. So be warned. Check out the rest of the fish in the tank as well. If there are dead fish then there may be something wrong with the tank, or this may be a new batch that has just been put in the tank. The dead fish are the weak ones who could not stand the shock of being moved. Leave this tank well alone.
Make sure that the fish that interests you is compatible with your tank set up and any other fish already in the tank. Don't be shy to ask. If you have a few species in mind before you leave for the fish store, you can check out fish species database to see if the fish you have in mind are compatible with your current fish and tank setup.
Now that you have bought your fish how do you travel with them? If you have walked to the shop then carefully carry the fish home in the carrier bag provided. Try not to "bump" the bag too much. As you can imagine, the fish are stressed enough already without you giving them a headache. If you have come by car it's a good idea to bring a bucket or a box with you so that you can sit the bag in it. Use the seat belt to secure the bucket/box to the seat. There you go. Take them home safely!
When you have reached home. Float the bag that contains the fish in your tank for about 20 minutes. This allows the water in the bag to become the same temperature as the tank water. After 20 minutes carefully open the bag at the top. Fold the top to produce a collar and scoop some water from the tankinto the bag. Re-float the bag for another 15 minutes. The collar has air trapped in the folds, which should allow the bag to float with out sinking. The introduction of the tank water allows the new fish to get used to the water quality of your tank. After 15 minutes you can carefully submerge the whole bagto let the new fish swim out into the tank. Don't be tempted to pour the fish in to the tank. Fish do not like being stressed. The new fish will need time to get used to their new surroundings and tank mates. Keep an eye on them for a couple of days. Here's a tip. Give your fish a little food at this time. This will encourage the new fish to mingle with the other fish.