I'm no stranger to a soldering iron.
For electrical work, first and foremost, make sure you use ROSIN CORE solder. The stuff that is used for copper pipes won't work.
Next, the thinner the solder wire (the actual solder itself, I use .032 diameter) the faster and easier it melts, and it is much easier to work with in my experience.
I also HIGHLY RECOMMEND something called "helping hands". It is a weighted base with a magnifying glass and two or more alligator clips attached to it. This holds what you are soldering so you have your two hands free to hold the solder and the iron.
As for soldering irons, I bought one at Radio Shack years ago and still does what I need it to. You don't have to spend too much money on one, I do recommend one that has replaceable tips, and use a finer tip like one that would be used for mounting a transistor to a circuit board. They heat up faster and are easier to control. I also recommend a sponge that you can wet down with water to clean the tip of the iron (globs of solder sometimes build up and stick to the iron).
Soldering 101: Tin the tip of the iron, put a coat of solder on the tip of the iron before actually touching it to any wires. This helps prevent oxydation and improves heat transfer. Heat the wires or leads, not the solder. Once the wires are hot (the solder will melt on the wires, not just the tip of the iron - this is where the small diameter solder comes in handy) put the solder on the wires and remove the iron. If you did it correctly, the joint will be shiny with a mirror finish. If it is dull or flat looking, you have what is called a cold solder joint. This is caused by the wires not being hot enough, which means you melted the solder on the iron, not the wires.
Here is an excellent video of the basics on soldering:
http://www.curiousinventor.com/guides/How_To_Solder
This video goes into a lot of detail and is thorough in its explanations of how and why certain things are done. It even addresses the potential toxicity of the fumes!:shock: I only watched a few seconds of it and I learned something new - and I'm an experienced solderer!
Good luck, don't burn yourself, and have fun!