You can buy wire strippers from your hardware store ranging for $2 to $20+. If you are uncomfortable with stripper thin wires, buy the more expensive stripper which pretty much gaurantees perfect stripping every time. The expensive strippers have locking mechanism and dedicate slots for different gauge wires.
There are also smaller heat shrink tubes made for the thinner wires. I think radio shack may still carry them. The wires you'll be using should be stranded and pretty thin so just twist them together, apply solder and shrink.