At Hackers this week, we learned how to solder. Group members stripped wires and then soldered them together, and they made LED circuits by soldering them onto stripboard, and tested them with Arduino programs.
As we discussed, it is important to build your circuits temporarily with a breadboard (where you just push the wires in, and can easily move them) before moving onto soldering them on to stripboard. Stripboard (also called Veroboard) has holes every 2.5mm in a grid, and has copper strips on one side connecting the holes in one direction. You mount the component (such as an LED on the side with no copper, and solder its pins to the copper strip. Then, you can solder a pin of a different component somewhere else along the same copper strip, and current can flow through the copper strip.
There are plenty of videos on YouTube to demonstrate soldering technique. Here is one by Emer Cahill of GMIT: