I tried to get a job at the range I go to and they told me the requirements are:
Need to know how to safely handle firearms and be able to teach others
Basic gun-smithing is a plus
Deal with the public
Disassemble, clean, and reassemble many types of guns without manuals
A lot of experience(Every range and shop I've been to the employees have had handguns on them at all times)
At least 21 years old(make gun sales and carry a handgun on their person)
And what Scolar Visari said is really good stuff.
In my experience gun shops and ranges tend to hire people they know or who are regulars, so getting to know the people where you want to work would be good. And if you go enough it can show them you are safe, responsible, and you know your stuff. 'Course somethings maybe different depending where you go and where you live.