This posting falls under tips & tricks. You could consider this pointers for the newbie from a newbie. So you're warned, I've learned all this over a period of maybe a week.
When I started putting together my CupCake 3D printer from MakerBot I found that I needed to learn some soldering. (I got it a generation or two too soon, not all the sub-assemblies were pre-assembled.) I took a guess on some training kits and tools, but found from the Seattle Robotics Society (SRS) workshop that I wasn't far off.
I started with a Learn to Solder Kit, turns out the same kit the SRS suggests for folks to learn how to solder. I found it had good enough instructions to get me started. However, instead of using the soldering iron that came with the kit I bought a Weller Analog Soldering Station. Among the folks at the SRS workshop the Weller was considered among the two better versions for circuit board work. I also bought a work stand since every person doing soldering in the Make Magazine videos has one.
One thing I did learn, the thick solder I bought is not a good idea for electronics. I learned from the workshop that it doesn't heat through quickly. One of the folks at the workshop ran with me to Radio Shack and helped me pick out silver-bearing solder. This type melts fast and wicks better due to the silver. I had tried the lead free solder that came with the training kit, but found that it behaved like I was told, it doesn't flow as well as well as the other solder.
In addition to which solder to use I learned that I didn't have my iron hot enough. Setting the Weller at a bit over 600ºF is the best. It'll heat up the area quickly and let you remove the iron from the components before the board heats up too much. That also explains why the desoldering wick didn't work when I did the lesson in the training kit, I was operating at too low of a temperature.
Another technique I learned is to touch the iron to the largest metal part that you're soldering to. That way the heat is conducted to the largest area helping to melt the solder better. You still have to heat the other part, but having one hotter makes for quicker soldering. The goal is to let the melted solder wick into the hole in the board, but not so much that it comes out the other side.
There are a couple of items I was told that I still need to get. The tinning technique in the training kit isn't enough. The tip tinner/cleaner compound from Radio Shack was recommended. One of the the guys attaches his to the top of his soldering iron power station. Besides that, a flux pen (Amazon search) would be a very good investment. Especially for desoldering since it helps suck up the solder into the wick even better. Unfortunately that's the next thing I need to learn well, since I messed up the assembly instructions.