Here's some BASIC info:
1. Antlers counted per side.
A "typical" mature mule deer buck has four points per side. Two front forks and two back forks. Unlike a whitetail who has one main beam that the points all come off from. Look at lots of photos of mulies until you can see what is a mature buck. Generally speaking the deeper the forks are the better.
A mule deer will generally start out a spike buck, then next year spilt to a "forked horn" then next year possibly a three point (in the west we count only one side at a time) so thats three points per side or variations i.e. "three by two," four by three, four by four etc...
2. Whats a mature mule deer.
A mature mule deer has four points per side (8 point eastern count). Western states vary on counting the "eye guards." Most dont. So if you see a mule deer with four points per side its a good one. Good luck.