The earlier presented Simple Arduino is a good design, but it is not so efficient in using space. There is a lot of ‘whitespace’ on the stripboard. With a little bit of effort a lot of space can be saved:
Choose a smaller pushbutton. Leave out the LED on D13, you know if your circuit is working or not. The illustration below is as seen from the component side
I have built the circuit on a board of the same size and it clearly shows how much room is left for hardware of your own choice. You will not find a powerLED on the circuit, but that is easy enough to add. You could also make the circuit even more compact by shifting the 7805, C4, C5 and D1 to the space left of the ATMEGA (and cutting tracks q,r and s ofcourse).