Since I haven't bought Neon for a long time. But I remember I bought some group of 6 or 8 like 2 years ago. Anyway, I don't think I lost any. So I try to come up some tips. Some may sounds like a common sense, forgive me.
First, get them from reliable source if that is possible. Like other aquarium hobbyst or breeder is good place. Perhaps, you can get from the aquarium society auction. Maybe next best place would be small well run local store instead of the big chain store. The reason for this is the big chain is all business and they TEND to have more staffs. And store employees turn around is higher than your local store. And SOMETIME I know more than the young high school looking clerk of the chain pet store. I'm sorry if I offend someone but generally speaking you know I am right. There is always exception but unlikely. And the big store tend to get the big shipment which could be good for the price. But I see lots of time, there are 100 neon in the tank and not all of them are healthy. I notice some have the famous white spots(ick) on their body. And there are some dead body if you check the tank often. And I don't think it is not a surprise that some "healthy looking one" is not actually healthy at all. When they are kept with sick or dead fish. Also, the big chain store tend to get Neon from mass produced Asian country. Which I have some suspicion of their hardiness. Do you know if you buy like 1000 of them from there, the each neon only cost like a nickle or a dime. That is why they can be replaced so easy. Even if they replace few times, they still make money. That is why they don't care or they expect some Neon to die in the tank of big chain pet store. And big store get shipment more often which could be good when you are looking for certain fish. But not so good, when you are looking for the fish that had some time to settle down after the long trip. Just like us, store experience that some fish die within the few days after the fish move. Some of them just can't make the trip or fail to adjust the new condition and water. So wait for at least a week after the shipment. By then, only stronger one left. And you do want the strong. Beside you don't want the fish die on you after you take them home even if they replace for free. You want the healthy happy fish in your tank, right.
And you know you should not get the fish from the tank with sick or dead fish in it.
Second, try to get the young and grow them up at your tank. I believe the younger fish do better adjust to the different tank than old. Beside, they are cheaper and it doesn't take long for the Neon to grow. Of course, you better make sure there are no big fish that have big enough mouth to eat small neon.
After all, most of the fish would eat the small fish that can fit to the mouth.
Third, go home as soon as possible after you got them fish. And acclimate your new fish slowly. Of course, you want to float the bag in the tank you intend to put in. Some recommend 15 mins but I would even go longer. That would balance the water temperature difference. But what about the difference in water chemical balance between the tank the fish used to and the tank you are about to put them in? You need to take little water from your tank water and put in the bag with the fish. Do this several times every 5~10 mintes. If the bag is small, you can put new water from your tank and take some out from the bag. Turkey baster is good for this. You can take your time. Longer the time and more time you change the water, better for your fish. It would be less shock and easier transition. Hence better survival rate. And finally, make sure to pour the bag of water and fish to the net so the water from their old tank would not get in to your tank. Since you do not want any paracite or disease.
If you follow these suggestion, I bet you lose less fish after you obtained.