Perhaps the most important point to take away from the video is that you heat the joint, then let the joint melt the solder.
In your kit, you will mostly be attaching non-stranded wires and component leads to terminals. Many terminals will have more than one wire or lead attached, so make sure the instructions specifically tell you to solder a terminal before you actually solder it!
If you are attaching an insulated wire, you will generally be instructed to strip it about 1/4". Then, you will feed it through the eye of the terminal and bend it to crimp it onto the terminal. It is important to make a good solid mechanical connection of the wire or lead to the terminal prior to soldering it. For one thing, a good mechanical connection prevents the wire from moving around on you while soldering. Such movement leads to "cold" solder joints.
As I have mentioned in the past, Radio Shack carries (or, at least, used to carry) 5-lug terminal strips very similar to the ones used in the kits. A few of these and some cheap resistors are good for practice. Just screw the terminal strips down to a scrap of wood, and have at it!
BTW, if the video guy tells you he is going to be taking extreme close-ups of your hands, it's always good to pop for a manicure!
