They have a hidden campsite high in the mountains, well away from where the Fire Nation likes to patrol. They limit their use of campfires and have a special ventilation shaft to dissipate the smoke over a wide area.
It's galling to have to be so cautious, but the Earth Kingdom's finest soldiers tried a straight fight and lost hard. They don't want to give up, but a straight fight is suicide... So don't give them one. They take turns dressing up as ordinary peasants, who are still around in a lot of the so called Fire Colonies to do the unpleasant work the new 'residents' don't want to. Go into town, do chores, and talk to people, watch guards. Identify particularly important or deserving ones.
And occasionally, they'll go down and ambush and kill one. If nothing else, it keeps them from reinforcing the siege of Ba Sing Se...
And so here is a clearing in the hills, and a cave that has gradually been improved on the inside by Earthbenders but is pretty unimpressive from the outside, and a dozen half-starved, angry young men and women.