The most effective way to warm flour or corn tortillas is over a gas burner. (Don't even think about warming them in the microwave!!) Just turn on your gas burner, a bit under medium, and place a tortilla directly on the burner. Flip frequently, after it's been on just 10 seconds or less, so you don't burn it. I just use my fingers, which requires a bit of dexterity and skill, but you could use tongs if you're worried about burning your fingers. Keep flipping until the tortilla is nicely browned in spots, and usually they will puff up a bit, then it's done. Don't worry if you have some blacker spots, it will still taste good. Adjust the flame if you need to, you'll get the hang of it.
You can either serve up the tortillas one by one, or put them in a covered tortilla warmer. Make sure to put a single paper towel in the bottom of the tortilla warmer first, so the tortillas on the bottom don't get soggy.
If your kitchen isn't equipped with a gas stove, you'll have to make due with a frying pan. Use a good heavy one, either cast iron or nonstick, DRY. This method doesn't require as much flipping, but you really should spin it around with your fingertips. I give my tortilla a quick spin every few seconds or so, until it's almost too warm to touch, then flip it and spin again for roughly the same amount of time. Again, I suppose you could use a set of tongs for the spinning/flipping, but why have another thing to wash if you don't have to?
I'd much rather wash my hands than more dishes.
Now that you know how to warm tortillas, go show off your skills and make fajitas or tacos (lamb or beef) or something.