Our normal procedure here on the open waters of North Florida is to slip up close enough to them, either at night with a light or just before dark or right after sunrise, and cast a light line with a snag hook over them. We use a spinning rod and 20 pound test Spiderwire for that.
This line we use as a "locater" in that we follow them on the trolling motor with it. Eventually they will come to rest on the bottom someplace. Once they do we use the "locater" line to get right up on them.
Once over them we then use a heavy rod, 80 pound test with a big stout snatch hook, and drop that down and drag it about till we feel gator. When you feel gator you set down hard on him. This is when it gets fun. Imagine 4 or 500 pounds of gator attached to the end of your line. Starting out maybe as close as 10 or 15 feet away. Even more fun in shallow water where you can see him kicking up all sorts of stuff.
With the heavy line you can now fight the gator. Once he settles down again, depending on how large we think he is, we will either hoist him to the surface and stick him with a harpoon or if he seems to be big we will set a second heavy rod on him and then haul him to the surface.
Once the harpoon is stuck good, it's tied off to the bow ring of the boat with 1/4 inch nylon, he's ours. Haul him to the boat and pop him behind the head with the bang stick.
And yes she and I do this alone quite often. Just us two on that one in the picture.
It's about as much legal fun as you can have.
And let me tell you, in the middle of the night, when you can't tell what you've really got snagged, and that thing rises to the surface right next to the boat, and you can see the boat in the picture and you can imagine how low it is in the water with two of us standing on the gunnels putting a bunch of pressure on a 4 or 500 pound gator.........well when that thing pops to the surface only a few feet from your feet........excitement!
There are other ways to do it, some folks use bait which is BORING, but we've caught loads of them over the last dozen years this way and it is fun. Five so far in the last 2 1/2 weeks of the season. Two of those five were as big as this one.