help with replacing outside hose spigot
Closing the inside main valve to your house should do the trick. If you haven't operated the main valve regularly do so with caution because gate valves are noted for failing when you close them. After doing so, check any faucet to verify the water has been shut off. If you live in a freezing climate you probably have an inside shutoff valve close to the outside spigot that you cold use instead of the main one. After closing the main valve, if it' a gate valve, you might find that it won't open back up and that the handle just spins. That's due to corrosion and the valve has to be replaced. If you have access to the street cutoff and the water authority has no problem with you turning it off there, that would be a good option. They could possibly turn it off for free while you change your spigot.