One of the most common issues when riding a bicycle is a slipped bicycle chain. Though easily fixed on most geared bikes, the process can seem a bit daunting. Mainly, make sure a shoelace or pant leg hasn't gotten caught in the chain and the track which the chain must run on is free of debris.
Fixed or Single Speed Repair
Often the chain contains excessive slack causing it to flip off. To fix this issue, merely extend the distance between the back hub and the front cog. Do this by turning the bike upside down and loosen the quick release or bolt of the rear tire hub. Holding both sides of the rear hub, press on the front of the tire to increase tension and then tighten the screws. Tighten the chain only a fraction of an inch so that less than 1/2 an inch of wiggle is present when moved either up or down.
Remove From Front Cog
Once the chain has slipped, remove the chain completely from the front cog. Push the tension roller of the rear derailleur forward allowing more slack in the chain. Once the tension has been eased and greater slack is allowed, the chain can easily be slipped off the front cog.
Resetting the Track
In order for the chain to function properly, the track must be running in the correct places. With the slack created from removing the front cog, run the chain back through the lower derailleurs tension roller and up through the jockey roller forming an "S." Next the chain should run through the rear cassette of the derailleur, though the specific gear does not matter. The chain should sit in this track without any twists, kinks, or slack.
Replacing the Front Cog
Push the tension roller of the rear derailleur forward once more to allow greater slack and reset the chain on the front cog. While doing this be mindful that the chain should pass through the front changer arm easily. It does not matter which of the front cogs the chain is placed in as long as it is not rubbing on the front changer arm.
Rotate the Pedals
Use the seat to lift the rear wheel of the bike off the ground. Rotate the pedals around watching the chain cycle. Often the chain will begin to flip into another gear acting as though it is going to slip. This is normal, since when replacing the chain it is often not set directly into the same gear as when the bike was being ridden. The chain should not come completely off, merely seat itself into the correct gear.
If the chain repeatedly slips off after riding or proceeds to make awkward noise, adjust the gear levers to be sure the changing arm is not agitating the chain. With small mild taps on the gear levers any noise should be alleviated. Recurring problems could indicate a kink in the chain, a link which is too tight, excess slack or a loose chain, or debris and gunk clogging the chains fluid motion.