How to change clock speed

I have an Arduino mega 2560, which has a default clock speed of 16MHz. I am using it with a serial baud rate of 9600.
I tried using the command:

CLKPR = 0x80;
CLKPR = 0x08;

This works to reset the clock speed to 1MHz, however, it resulted in the serial output to be strange symbols at every baud rate option.

How else would I change this to 1 MHz? And how would this affect the serial baud rate/ input/ output?

Thanks!

Please post a complete minimal sketch that demonstrates the issue.