Turn off the power to your breaker panel. There should be a large switch on the top of the panel itself. With larger panels, the switch will be outside, in the same box as the electric meter.
Unscrew the terminal screws for any wires in the 60-amp breaker, and pull them out. There are probably two, and they are probably black, red, or both. Keep track of them; you’ll need them later.
Pull the breaker out of the socket. Some firm pressure should slide it right out.
Slide the new 60-amp breaker into the slot where the old one was. Firm pressure should slide it in securely.
Replace the wires you removed before, and tighten the terminal screws to secure them.
Turn the power to your breaker panel back on.