Repairing a bike inner tube is not only simple and cheap, but it's also mandatory in respect for the environment. Indeed a punctured tube can be repaired many times before being thrown out. A different matter is when the tube is cut or the valve leaks, since it's more difficult repair the tube. Anyway most of the times the leak is caused by a nail or a thorn, and the hole is very tiny.
Although many of you already know this process, I'll explain how to easy add a patch to a pierced bike inner tube.
Step 1: the necessary
All you need is a pump and a repairing kit. I take for granted you already know how to remove the wheel from the bike and the tube from the wheel, so I don't deal this topic here, ask in comments if you fall in some obstacle.
The repairing kit is composed by some patches (probably of different sizes), some scratch tools (sandpaper or a little metal grater), a little tube of mastic (a type of glue) and maybe some little rubber tubes to spread mastic.