How do I temporarily plug a broken outdoor spigot?
Depends if you can use a wrench or not, or if your house was plumbed sensibly...

If your house was plumbed sensibly, there will be an additional valve somewhere in the house, generally near the hose spigot, that will shut off only the water to the spigot, not the whole house.

If not you need to unscrew the broken spigot, and (depending on what sort of threads it has) put on a cap or put in a plug. Or just put on a new spigot.