You need to replace the spigot. The stem is broken where the handle would go. In what part of the country do you live? (does it freeze where you live?)

Yes it freezes here often. Its in upstate New York

You should check and see if there is a cutoff valve on the inside.

I'm in Minnesota. Most, or rather I would think all homes here have a shut off valve inside for winter, usually one on/off valve for each spigot to shut off the water going to the spigot outside. Otherwise the cold can follow pipes with water in them inside and freeze and bust pipes inside. Mine area located on the pipes in basement in the ceiling about 10-15 feet from where they go outside, just depends how builder had it plumbed. And yeah you need a whole new spigot, or at least repaired. The top round part the handle is busted off. You may be able to turn water on by turning that top nub with a pliers and find valve inside to turn water in from inside, but it's probably best not to mess with unless you know what you are doing. Where it points down there is just something screwed on the spigot/where the water comes out. It's probably screwed on too tight or cross threaded. That happen to me and it was some kind of quick release thing that was busted and stuck on spigot and water wouldn't come out with it on there. Maybe some penetrating oil and try to unscrew, but support the spigot/part that goes into house so you don't damage it...but probably best to just get it replaced.

Kind of funny story. I noticed my neighbor only used one of the two water spigots outside. I finally asked him about it. He said it never worked since he moved in two years ago. I asked him if he knew about the turn on/off valve in his basement. Nope. He was using the spigot the next week. I did clue him in on turning off from inside for the winter and the importance of opening the outside valve to drain so his pipes don't get frozen water in them and burst inside house.

That black thing is a vacuum break. When you turn the water off, you rotate that black ring and it creates an opening which lets air in and water empty out. In that picture of the frost free unit, it's the black thing above the knob.

weedmeister, I'm pretty sure in this case the "black thing" on the OP's photo is just the female threaded collar fro the piece below- which I'd almost bet was a shutoff (we can't see it completely). The idea being that the knob was broken from the first shutoff and so they added another one.

No, I've used these before. The tabs on there are so you can push the 'ring' round and open a slot to the air.

Huh. I have a quick-connect gizmo that has a black collar like that to help screw it on to the spigot.

Either way, there is a standard female on the bottom end of that thing so it shouldn't affect usability of the spigot with a regular hose, if OP can get it to turn on. At least till it gets replaced.