These are not too tough...I have done this a lot with our coleman camping lanterns.
Pick up some new mantles from your local hardware or camping store and follow the directions on the package.
While your in there you should also remove the glass panes and give them a cleaning.
Call REI or Handy Ace Hardware in Tucker to see if they stock those. Easy to do...if not, I'm out your way all the time
Gas lanterns are very beautiful in the ambiance they create. Have you ever thought about adding professional low voltage outdoor lighting to your home to heighten the lighting effect?
I would like to second HandyAndy's suggestions on the fix.
Finally got the gas mantles - love Ace! Do we shut the gas off at the meter to change mantles out?
@Carol should have turn on/off in basement
The local shut off at the lamp should be fine. Once the mantles have been "burned" you will need to light the lamp with the gas on and allow it to "season" a bit. Keep in mind that once the mantle have been burned they are pretty fragile.