How do I replace a broken outdoor faucet handle on my hosebib?

There should be a screw holding the handle on the faucet. Unscrew the screw and the handle should come off. Take the handle to Ace Hardware, Home Depot, Lowes, Menards, and they should be able to match it for you.

Thank you for your response, I cannot remove screw as it is stuck and when I turn it water comes out of spigot. I think I have to remove the whole outlet but having difficulty.

Turn the water off at the street. Take a rubber band and put it over the screw then put the screwdriver on top of the rubber band. This will add a little friction, it is going to take some pressure. Then take the handle, and the screw with you to the hardware store. There will be someone who will make sure you leave with the right things. Also you may need a washer, or rubber gasket, i'm not sure.

You can also tap the screwdriver with a hammer to "seat" it, making it easier to turn. Be careful not to strip the screw. Maybe use a little WD40 to loosen the screw.

The screw should either be brass or stainless steel. It shouldn't be rusted. It's probably very tight. I use "Penetrating Oil" which over time will get down around the screw. Another method is to put the screwdriver in the screw and tap the top of the screwdriver lightly for a minute or so. Also, by taking a hair dryer and heating up the faucet while holding ice on the screw. This will expand the faucet and contract the screw.

I find PB Blaster works quickly on corroded/tight threads

Actually hose bibs are rather easy to install if they go into a basement or crawl space you can easily access. They come with piping that goes all the way through your wall. With the next compression connectors there is no need for soldering anymore. Go to your local home center or hardware store and ask the assistance. They can show you how easy it is.