Many of us here in magazineland don't run bead-lock wheels. The problem with that is that we still air down when we are wheeling, often to 8 psi, which means we tend to blow the tire bead off the rim with some regularity.
"Psssss" tends to accompany the sensation of one corner of the Jeep sinking, and sometimes even a burst of leaves getting blown away from the tire. Usually, it's the tire that is hardest to get to, but whatever tire it is, it's not the end of the world.
The first thing to do is get the weight off the tire. In this case, we removed it, but it's often just as easy to jack that corner of the Jeep up and re-seat it on the Jeep. After the weight is off the tire, make sure the bead surface is clean of sticks, mud, sand, or rocks. If it's sand or mud, use whatever liquid is necessary to clean both the surface of the rim and the corresponding part of the tire. If rocks or sticks are stuck in there, pull them out.
When you get down to it, the only tool you really need to fix this is an air source. Onboard, engine-mounted compressor, electric compressor, or a carbon dioxide air tank, it doesn't matter as long as it puts out air (the more the better). Sure, other tools can make it easier, as noted later in this story, but the only strictly necessary one is an air source.
Simply put, the more psi and volume you can supply, the easier the tire bead will go back to its home against the edge of the rim. We've done it with as little as 35 psi, lubricated the rim with some ATF, and it oh-so-slowly went back on. Normally, 80-120 psi is more likely to do the job.
After cleaning it with whatever is available-be it spit, water, antifreeze, ATF, and so on-we will usually remove the valve stem core. While not strictly necessary, we've found that removing it makes the bead seat that much faster. More air can get into the tire without the core in the valve stem, and that means more air pushing on the bead.
Whatever your situation, if you are wheeling with an air source (doesn't have to be yours), here are a few tips to help you get the tire back on the rim and continuing on down the trail.
This is another of those unnecessary steps, but we notice that it helps. Take a ratchet strap and put it around the circumference of the tire, then cinch it down hard. This helps to push the bead toward the rim making it easier to seat. Two or three close friends can be substituted for the ratchet strap in a pinch. Be sure to remove the strap once the tire starts filling with air. | 
Even with the ratchet strap, some persuasion can be needed to coax the tire to seat while hitting with as much air as possible. In this case, we had removed the tire from the Jeep and had to push down on the rim while pulling up on the tire. If we'd left it on the Jeep, a simple pull on the tire while putting air in it would've done the job. | 
Once a "pop" is heard, no more air escapes the tire and there is no space between the rubber and the rim, the tire is seated. If you've pulled the valve stem core, now is the time to put it back in. Make sure it's clean (no oil here-spit or water only as needed) and put it back in. Then fill the tire to whatever pressure you desire. |