Start off by being a solid deputy who is a worker and team player, is a gun guy, expert shot (we don't get marksmanship badges/rankings, but all of the instructors would qualify as expert), patient and wants to instruct to help your fellow deputies, not just for the free ammo. (Hint - instructors only shoot on training days on their own time after everyone else has left. Most of us go to the public range on our days off and pay for the range time.)
Put in a request with the firearms team sergeant to be an instructor, and start out by being an assistant. Assistants help watch the firing line for safety issues, usually know enough to help instruct on some basics and will run some courses of fire.
If you are qualified (if you've gotten this far, you usually are), you will be sent to a firearms instructor school when a slot is available. Some of us have been to the 40 hour FBI handgun instructor school. Others go to an 80 hour school which covers handgun and shotgun and maybe rifle. (I went to the FBI school - outstanding training. We shot, but not as much as I expected. The bulk of it was oriented toward methods of instruction, lesson plan development and methods of remediation.)
Armorers don't have to be instructors. Just be a gun guy, again a worker, take care of your equipment and ask to join the team. I've been to Glock armorer and MP5 armorer, and since I'm part of the HK family, I hate you.
Glock & HK MP5 armorer