How do I replace a broken outlet safely at home?

Turn off the circuit breaker for that outlet and use a voltage tester to confirm the power is actually off before touching anything. Remove the cover plate and unscrew the outlet from the electrical box. Take a photo of the wiring before disconnecting anything so you have a reference. The wires connect to specific terminals: black wire to the brass screw, white wire to the silver screw, and bare copper or green wire to the green ground screw. Attach the wires to the new outlet the same way, push it back into the box, screw it in, and replace the cover plate. Restore power and test it. If you see more than two wires or anything unfamiliar, call a licensed electrician.