I recently acquired an Arduino Uno for use in some of my classes at a local college. I can program the Atmega328 and everything is fine. Once I take the chip out of the Arduino it requires an external crystal to control the clock. I know there is a way to enable the chip to run off of the internal clock, but after searching the internet I still haven't been able to find how. I found an article: http://arduino.cc/en/Tutorial/ArduinoToBreadboard but the instructions don't work for the Arduino Uno.
Get the data sheet for the particular chip you're using. There's a section on which bits of which fuse bytes need to be set to configure features such as this. I can't stress enough using the data sheet as the ultimate reference. Be very careful following guides. Take the gist of the instructions, but never copy the fuse settings from an example, as it may not do what you think it does.
The method by which to actually set the fuses is just a simple command line from avrdude. Here's a guide I found once while researching it: