A healthy fish will respond when picked up. You might want to tap the side of the cup (ONE OR TWO TIMES!!! No more!!) as well. If they don't respond and start swimming around, they're unhealthy. Most fish won't just be swimming all happy-like without some kind of interaction. They won't have cotton-like patches on their head or other parts of their body, a (thin) black outline of their fins, or appear bloated. If their scales point out, DON'T buy the fish. If they can't seem to swim straight, they're unhealthy. Their fins will be smooth and not jagged.
Names come with the fish. I personally don't like the name "Donald", but it fits one of my fish perfectly, so that's his name.
Some oranges/purples turn out red, black may turn blue or purple, and pink may turn red. They usually darken a bit when you get them out of the cup. One of my fish, who I bought as white, turned BLUE, so you never know!
Get the fish that speaks to you (not literally... if they do, you might want to get some help). If you don't find one that you connect with, don't be afraid to just leave and come back in a week's time. They usually get a new shipment once a week.
Make sure you have good supplies! A 5 gallon tank is preferable, but 1 gallon is okay (but you must clean it once a day). A heater/thermometer is ESSENTIAL. Filters are pretty much optional, but if you want to get one to cut back on water changes, make sure you get an adjustable or low-flow one. Shells can mess with the pH balance, but most decorations in Petsmart are going to be okay. Gravel is porous and can old in bacteria, but it's okay if you rinse it really well with hot water. ALL decor must be rinsed with hot water before you put it into the tank. Plastic plants are a no-no. They tear the fins of your fish. Silk plants are okay if there are no metal pieces. Make SURE you get a water conditioner! I recommend Tetra's Safe Balance. Don't get anything with additives like aloe vera or "color enhancer". They can dirty up your tank. Tap water with conditioner is the very best water you can use, so don't waste your time with bottled "fish water". A water test kit is preferable, and can help you if your fish fall mysteriously ill. Do NOT buy fish flakes or pellets that do not say "betta" on the front. Betta pellets are a must, and buying frozen brine shrimp/bloodworms is preferable. Freeze-dried foods can tear the digestive tract. They will probably have a freezer with these foods near the fish aisle. DO NOT GET A NET. Use the cup if you need to catch your fish.
Make sure to acclimate your fish. You can't just dump your new fish into new water.
1. Put your fish into a zip-able bag (a sandwich bag is fine) along with all of their original water. Some people use the cup, but it's much easier to acclimate with a bag. You can (and probably should) leave the bag open. If you need to close it for a bit, you can. You fish could survive a few hours like this.
2. Fill your tank with enough (conditioned) water to be about even with the water level in the bag. Make sure that it's at least deep enough for your fish to swim straight. Set the bag into the water. This is where I usually open the bag, when I'm sure that it's stable. Wait 30-45 minutes at least. An hour is best.
3. Use a cup or turkey baister or whatever you have and put about 1/8-1/4 of a cup (you can eyeball it, it won't hurt your fish if it's a bit much) of the new water into the bag every 15 minutes. At first, use a VERY small amount, but you can work your way up.
4. Once it's been about 2-4 hours, or the bag is getting hard to stay up straight, you can put your fish into the new water. You don't need to raise the water level. Your fish has probably been in the cup for a very, very long time and isn't used to being in deep water, so he might feel uncomfortable or frightened.
5. The next day, do a full water change (the little floaty bits from the cup is in that water... ew) by catching him with the (rinsed) cup that you bought him in and pouring/siphoning out all of the water. Put new water in and condition it. You can fill it up completely now. Let it sit until it's the same temperature as the cup water. Release your fish into the new water.
And... you're done!!
Good luck! It is VERY exciting and fun to buy a new betta! (Lucky...) :D
Sally, I will always love you. You were my babygirl and the gateway to my bettabug. Thank you.