Although archery may have a 50,000 yr. old history, I think that we can be fairly certain that bowfishing wasn't what they had in mind. Bows and arrows were hand-made and much too valuable to take a chance on loosing or breaking one on a fish, although I'm sure they did whenever they had to. Nets, even though primitive, would have been much more effective.
Most states allow bowfishing of the so-called "rough" fish. Those are suckers, eels, perch, gars, carp and the like. Gars and carp are the most popular and usually the most plentiful. Check with that state's DNR to find out what you can harvest.
Carp can be found in almost any body of water, large or small, year round. The best times are during the spawn in spring or after some good rainfall when the water in the shallows is deeper. The only things needed are bow, arrows, and waders. At times the fish can be so involved in spawning, the bowman can walk out among them and shoot. Some bowfishermen use field arrows so that they can just flip the fish onto shore without having to disengage the barbs to get the arrows out.
It's usually necessary to stalk carp. They are usually fished in shallow water, and although muddy, they can detect shadows and other movement from quite a distance. Experienced bowfishermen know they must take advantage of tree shadows and other cover and MOVE SLOWLY.
After a shot, regardless of a hit or miss, you'll have to wait awhile for the fish to return, or move to another spot. As soon as an arrow hits the water, the fish spook and head for safety, especially if you hit one. If you don't move, they may return. After 15 minutes or so, forget it. Move.
On small rivers or streams, it's possible to get some action by moving quietly and slowly along the banks. You'll need polarized shades though. On lakes and rivers, a flat-bottomed boat is the way to go. Ideally it'll have a raised platform for better sighting and angle on the target. It's better with 2 or 3 people. One person to position the boat while the other fishes. At night you'll need a light at the bow of the boat, or someone to shine one on fish.
If the fish are deeper, they can be sometimes lured to the surface with bits of bread or kernels of corn cast out on the
water. You'll have to be ready, because most likely you'll only get 1, possibly 2 shots at a school of them.
Your aim doesn't have to be perfect, because a hit almost anywhere on the fish will sink a barb. Then pull it in easily. They can't be horsed-in like with a rod and reel, because it's to easy to tear barbs out of the soft flesh. Some bowfishermen tie their line to a rod and reel so they can have fun playing them out that way. Since a perfect aim isn't necessary, this is a good way to introduce beginners to the sport of archery fishing.
The arrows are usually heavier than target or hunting arrows, and normally don't have feathers because you're not shooting that far. Heads are barbed, either retractable or rotating. The line should be 80# test, braided nylon depending on what you're after. There are several different types of reels available, manual and retriever type.
The most important thing is SAFETY. Always be aware of your surroundings and if anyone else is in the area.