Using the ATMega168 chip externally from Arduino

First, what your asking requires a familiarity with straight AVR development at least to a greater extent than just the Arduino managed environment.

The arduino uses a 16MHz clock--the internal clock on the 168 is limited to 8MHz. The change is possible but not really straight forward.

To program the 168 to use its internal clock is simply a matter of changing the fuses. Look at the documentation for the arduino programing software (AVRDUDE?) and the data sheet on how to do this.

After (or before this) you'll need to modify the Arduino environment and libraries to use the different clock speed from 16MHz. There have been some messages on the forum on how to do this.

On the other hand if you include a 16Mhz resonator (1 part) you could move your 168 to a breadboard after programming with the regular board. Personally I would use the resonator rather than introduce the complications of rebuilding the Arduino environment.

If you really want to use a different clock speed you can use the Arduino as a programmer (writeups elsewhere) and learn to use the underlying GCC (or WinAVR) to develop your application. More flexibility but a greater learning curve.