I would feel shy of asking someone to shoot their gun on the range, but by reading some posts here, I assume it's more or less a common practice. I will try that.
You most likely won't need to ask to shoot their guns. I never ask someone if I can shoot their gun. But I get to shoot lots of others. Just go up to someone, ask them what gun they are shooting (if you don't know) and ask them how they like it. Then tell them you are looking into buying a new gun. At that point, there's a 90%+ chance that they will then say "you want to try it out". Then you just grin and say "Sure!"
Then be sure to pay it forward when someone asks you about your gun someday!