Every tank is different. Most pet stores will tell you a fish for a gallon of water. It mainly depends of what type of fish you have. Some fish can with stand being crowded, but others may die if there isn't plenty of room to move.
Guppies are great fish especially for children. They can live in any size tank, any temperature, and can survive in crowed tanks. They take very little food to live, and if someone forgets to feed them they eat the algae off the sides of the tank. I have had as many as 100 or more guppies in a 10-gallon tank at one time. You couldn't even see through the tank hardly. The down side to that is they start to eat the baby guppies.
It is best to not over crowd your tank, because it will get nasty. You will have to clean it more often than if it had fewer fish in it. If you do put more than ten fish in a 10-gallon tank buy some algae eaters, and real plants. They will help maintain the atmosphere of the tank. Also if you have a good filter system and chemicals for the tank that too will help balance out the tank even if it is over crowded.
If you have small fish you can put more into a 10-gallon tank and not harm the fish, but if you have big fish I wouldn't put no more than ten in the tank. The bigger fish need more room to move about than the smaller fish. So it would depend on what type of fish you are buying that would determine how many can go into a 10-gallon tank. I would advise looking up the type of fish you want on the Internet and find out what kinds of environment they can live in. It would tell you if they can handle being in a crowded tank or not. Then you can go from there. You will be able to make a better selection if you know what type of fish you are buying.
Make sure you have everything you need if you are going to put more than ten fish in a 10-gallon tank. If not you will be wasting your money. Without the chemicals and plants to balance out the tank it can become unstable, then your fish will die. With fewer fish, they have more of a chance at living if the water happens to become unstable. The more fish, the more of mess if the tank is off balance. Having to many fish will make it harder to get the tank back to normal. I would go with the ten just to be safe.