How to take my Atmel328 Off Arduino Uno and into separate Circuit

Thank you terryking228, I think I understand that a little better now..

You say a stable 5V source.. I'm kinda afraid to ask, but what are batteries considered? Most likely unstable as they loose voltage as they discharge right? Could I fix that with a voltage regulator, and use a combination of batteries that give a higher voltage than 5V?

I can't see where the resistor goes in the part about the oscillator in the diagram?