Do a search on google, and you will find lots of tutorials for soldering. This is something you are only going to learn by trial and error.
I'm not sure how much you already know, but some of my first mistakes when I started was that I was using a soldering iron tip that was severly oxidized (blackend) and solder wouldn't stick to it or melt quickly. I also was using solder that was to thick (I now use very thin mostly silver based solder). And bought a new tip at radio shack for like $2. Learn to keep the tip clean and "tinned" with a thin layer of solder covering it (clean away excess solder off the tip by dabbing in a small damp sponge).
You may also notice it feels like you need 3 hands to do it correctly. One to hold the soldering iron, one to hold the wire, and one to apply the solder. It really helps if someone else holds the wire for you, or if you get one of those mini clamps called "helping hands" (radio shack sells them, they help hold projects and look like a pair of aligator clips and magnifying lens on a weighted stand).
Make sure the copper contact is clean and shinny. Put the wire on the surface, and heat up the wire and copper surface at the same time (iron should be touching both). Leave it there for a couple seconds to heat both up, and then touch the solder to the wire and not the copper surface (while keeping the iron on both surface and wire). The solder should melt into the wire and then "onto" the surface. Use enough solder so you get a little hershey kiss type looking solder joint (that is shinny).
-Dave