I recently started playing and have a lvl 12 tauren shaman.And I have been wanting to run a dungeon with my friends one is a warlock and the other is a warrior. I know that the first dungeon I have access to is Ragefire Chasm but I was wondering what level we should be at to run t with just the three of us?

probably about 13 or 14 with the three of you.
Although you could take it down right now with some organization (class roles, buffs, etc).

Thanks

Does anybody have some advice for actually running the instance?

At that level with just three of you, you need to watch your pulls.  It's a fairly simple instance but your tank will not have alot of aggro grabbing abilities so the lock will need to focus on the same one as the tank and be careful about dotting the whole group.  If he gets aggro he'll most likely die followed shortly after by the other two of you due to not being able to drop the mobs quickly. The best way to pull at this level is for the tank to use a ranged weapon. I would suggest no more than 4 mobs at a time and you should be ok.

keep in mind most instances are designed with 5 persons in them in mind. one tank, 3 dps, one healer. so you may want to take more as one for dps. but it depends a bit on what the persons in the group are comfortable with.  if the tank and healer are somewhat experienced and the dps is new, its a different story as when the dps is experienced and the healer and tank have no clue ;)