After playing with your Arduino for some time, you may think:
"What if I want to use my Arduino for something else? I don't want to leave it behind in my project. What do I do?"
The simplest answer to this is to re-create it on your breadboard, at least to start with. That way, if you do mess up and make a mistake, it's easier to correct.
Do bear in mind that there will be (most likely) no way to program your ATmega chip once removed from the board. If you want this functionality, you'll need to use an ICSP system or a FTDI cable, which is beyond the scope of this article at this time.
Please note that you can use 0 ohm resistors as jumpers if you want to. (Some kits use them instead of wire).
(Assembly instructions to come. Refer to here in the meantime.)
You can find all these parts yourself, if you wish to save money, or you can buy the parts as a kit. oomlout do one here, if you live in the UK. Solarbotics Ardweeny is a similar kit from Canada. Barebones Arduino Circuit Kit is a similar kit from the U.S.