I need to know how I can do a back handspring without a spotter?

Answer 1

You need to learn it with a spotter first. After your coach says you can start doing them on your own, you just need to get your thoughts in order and know that you can do it.

Here are some drills to be working on:
http://geocities.com/aescougarcheer/basics.htm#td

Answer 2

you need to get in a tumbling class at a gym near your area. because back hand springs can not be self-taught, you need to be spotted first. trying to do this trick by your self could result in a very bad broken arm. trust me, I have seen many breaks, and they are not pretty.
get to a gym stat and start taking tumbling classes.
do not get discouraged, it takes time to build the strengh and perfect the trick.

hope this helped!