Simply push out the pins of the damaged link, then fit the joiner. If several links need to be removed, remember that you've shortened the chain when you get back on the bike, and avoid the big ring/low gear combination as it may well lock up your gears (or, worse, rip off your rear derailleur).

 

As a general note, it's always a good idea to carry a few spare links of the same chain you use, plus two Sram joiners; this enables you to replace whole sections of chain without losing overall chain length. I don't, however, recommend you try to use genuine Shimano joining pins as they require a very high-quality chain tool and can damage the chain's outer plates if fitted incorrectly, leading to another broken chain further on down the trail.  With all repairs, keep it as simple and easy as possible.
 
If the cause of the chain break is the derailleur going into the spokes, straighten the wheel by loosening the neighbouring spokes. If the derailleur and hanger have also been damaged, try to bend them straight-ish with your hands. It might be scary, but if you're miles from anywhere and you've got to get home; what else are you going to do? If your gear cable has broken during the incident, just leave it in the smallest rear gear (unless you have rapid-rise, in which case you'll be stuck in low) but you've still got the three chain rings to get home with.
 
In extreme circumstances, you may need to bypass the derailleur altogether. Run the chain on the mid-ring and a middle rear cog which allows you to achieve decent chain tension (you'll obviously need to shorten the chain considerably) and discover the wonderful joys of the simplicity of a single-speed MTB on your return trip.  If you have a dual suspension bike, lock out the rear shock if possible (otherwise pre-load the shock as much as possible), leave a little slack in the chain (not too much) and pedal gently.  Now try to get home 'cause your day is unfortunately officially over!