I am having a problem with my riding mower. The blade is not turning and I have to replace the belt but when I replaced the belt once before the new belt frayed and came off. I have a new one and don't want this to happen again.

Sounds as though the belt was not inside of a belt guard (or keeper). At the pulleys some of them will have a guard, or keeper that you must get the belt inside or it will quickly ruin the new belt.