www.applesnail.net is a great resource.
Mystery snails have differing sexes unlike most snail species who are hermaphroditic. If you get two you may get eggs laid just above the water line. If you do not want to raise the baby snails you can merely scrape this egg sac off and dispose of it.
Mystery snails do best in lower temperatures but do fine in tropical temps as well. They need a good source of calcium and minerals so hard water is better for them. I would check the pH and gH/kH of your tank just to make sure your water isn't too soft. Generally speaking most public water sources have enough minerals for snails.
Other ways to get calcium to your snails is by feeding them veggie wafers or sticks supplemented with calcium as well as fresh high calcium veggies like spinach. A good rule of thumb is to give your snail food twice weekly and remove it the next day so to not foul the water.
Snails should be acclimated just like fish, first by letting them acclimate to the temp and then slowly acclimated to the change in water. If you buy the snails locally you won't have to acclimate them as long as you would if you got them from another place.
It can take up to a week for them to come out of their shell and begin moving around. Going to a new tank can be stressfull for them but they aren't dead so don't mistakenly throw them out. To know if a snail is dead you have to smell it.. or it will be hanging outside of its shell. If it's on the bottom in it's shell chances are it's just hibernating.
Umm.. lemme think of anything else...
Oh.. if you find that your betta (or other fish) are eating the snail food you can easily remedy this by floating the snail in his own cup with his wafer overnight so he can eat without being bothered.
Let me know if you have any more questions.