Make sure you don't loosen any screws that might hold the fan in the power supply. Usually, the screws that are nearest the outside edge of the case are the right ones. Lift the power supply out. You might need to fiddle with it to get it out. Don't be afraid to really yank.
Power supplies are very sturdy.
Stick the new one right where the old one came from. Just line up the screw holes and tighten the screws in place. Replace the bracket that holds it in, if your computer has such a thing. Reconnect all the wires. Just the reverse of what you did to remove them.