Desoldering is the process of removing solder at a joint to disconnect two components, wires or materials. You might have to do this if you want to replace a component that's gone bad, or if you want to change something about your design once it's already soldered into place. To desolder wires you can usually just heat up the connection and wiggle them around until they come free. Better yet, if you have the slack, just cut the wire at the connections, strip, and resolder as necessary.
With leads that are mounted through holes on a circuit board it takes a little more finesse. To desolder something delicate its best to use a desoldering pump, or bulb which will actually suck up the molten solder and remove it from the joint. Soldering wicks or braided copper wire also work well to suck up unwanted solder. For more complete guides on desoldering check out Make Magazine's Learn How To Solder Skill Building Work Shop Video
and this site here
Soldering is pretty forgiving, and its usually pretty easy to fix a mistake. If you put down a little too much solder or position something incorrectly you can usually reheat your joint, melt the solder, and then reposition your component as necessary. Solder can be heated and cooled as many times as you need to get your joint the way you want it. So don't be discouraged if it takes you a couple of tries to get it down - you will still end up with a good connection if you stick with it.Extrapolation:
Soldering is a pretty straight forward process but there is no limit to what you could create with it. Try to join things together. It works well for making jewelery, doing basic arts and crafts with small metal objects, or re-wiring your toaster into a heating element for an infra-red sauna. If soldering has been keeping you away from experimenting with circuits or making a project, hopefully it doesn't have to anymore. Once you do it a few times you might even start to enjoy it.
If you would like to get started on a few basic soldering projects check out instructables user Makekits
and the Make Magazine Store
to build things like a MiniPOV
or a Daisy MP3 Player