You can pop out the chip, drop it on a board with some caps and a resonator/crystal and you're off and running.
Note, barnurubble, this only applies to pre-bootloaded chips; if you wanted to use a "bare" chip (say something from Mouser or Digikey), you would need to program it with a bootloader your own self. Given that you are asking these questions, this is probably not the task for you at your current skill level; leave it for another day.
You can purchase, however, pre-bootloaded ATMegas from several suppliers; I recently bought a few 328s from CuteDigi; there are many suppliers out there.
In both cases, you will need the caps, resonator, crystal - and if you want to program the ATMega after it has been removed from the Arduino - you will need some header pins and an FTDI cable or breakout board (or equivalent; there was a discussion here on the forums about adding USB for $1 to a standalone using a special cellphone cable).
When you put your ATMega onto your own PCB, use a socket - DO NOT SOLDER IT IN PLACE. Should something happen in the future, it will make replacing it much easier.
If you plan on doing this a lot, though, the socket on your Arduino board will suffer in short order, as the sockets aren't designed for a lot of insertions and removals of ICs. What you will ultimately want to do is either a) look into ISP programming, which is the same thing as is used to get the bootloader on the chip, or b) look into building a ZIF socket (zero insertion force - basically a socket with a lever, same as on a PC motherboard for the CPU but designed for smaller DIP ICs) onto a prototyping shield (or a custom PCB), and use that with another Arduino board or your own layout as a standalone programmer.