Broken Derailleur Cable
If your derailleur cable breaks while you are on the trail, you will still be able to get home, but only in a fixed gear. When this happens you need to put your chain in a desired gear that fits the terrain you are riding and screw the high/low adjustment screws until the derailleur is lined up with that particular cog.

The spring tension on the derailleur allows you to lock your bike into a single gear. For the front derailleur adjust the low adjustment screw into the desired chainring positioning so that it will hold it in that spot.

Broken Derailleur
You can convert your bike to a single fixed bike if the derailleur has broken. First remove the chain and then remove the derailleur with a 5mm Allen wrench. Place your chain in the middle chainring in the front and the middle cog in the rear. Using your chain tool, remove as many links until the chain is as snug as it can get around the drive train.

Loose Crank Arm
A one key crank bolt is an Allen bolt that threads through a special cap and on into the end of the spindle. With a one key crank bolt, you can tighten your cranks with a 5mm Allen wrench. Additionally, a one key crank bolt also works as a crank puller. Since the bolt is not flush to the crank arm it does require frequent tightening.

If you have standard 14mm crank bolts and you don't have a 14mm crank wrench with you take a small crescent wrench spin the bolt tighter. To facilitate getting the bolt tight, you might want to pound on the crank arm with a rock. The further you can get the crank arm onto the spindle the longer it will stay in place. Be careful when using a rock on your cranks, they will damage easily.

Loose Headset
If you have a threadless headset follow the detailed instructions. If you do not have compact headset wrench you will have to use your hands to cinch down your headset. Grab the top of the headset and twist the locknut clockwise. Hold the front brake and wiggle the front end and try to tighten. You may have to stop and do the same process over and over again.

Torn Tire Sidewall
The standard way of fixing a slashed or torn sidewall would be to place something inside the tire in between the tube and the sidewall to keep the tube in and the elements out. Place the material inside the tire carefully so that it will stay in place while you inflate the tire. I have known of people using a folded over dollar, power bar wrapper, sandpaper from your patch kit, or the large patch out of your patch kit. Gray duct tape is the best solution, wrap some tape around your tire lever.