What's on an Arduino board? Can i build one of these boards myself?
When I first built my first Arduino clone, I fount very useful the Fritzing examples (boards and schematics). http://fritzing.org/home/ 

Mind that in order to upload sketches, an FTDI module is very handy (unless you use ISP via another Arduino board).

In any case, I should recommend you to build an Arduino clone on a breadboard, before trying soldering. 

Good luck.

Additionally, you may use this picture (this is how  I create an Arduino on breadboard):



External power (battery) is connected to the screw pins (bottom left of the breadboard).