First-- Unplug the Mains Cable.
Replacing the power supply is a simple matter of unplugging your connections to hard drives, floppy drives etc. (Suggestion--Before you unplug them , make a mark on the drive and a mark on the cable to ensure corect re-connection)
Remove the power supply is usually just 4 screws at the back of the computer and lift it out
350 w should be ample for most systemsor you can get a bigger output if you want..
Before you buy a new PSU, can you borrow one from a friend to test your machine, as this may not be the problem.