Both bowfin and gar are extremely easy to fish for. Bowfin you want to use the largest worms available and put all of it on the hook. Drop it right to the bottom and wait. You will be battling with catching catfish as well but can almost guarantee a bowfin. This has worked mid day in my expierience as well as at night. I always fished near structures, a culvert outlet involving a weak current was always the best.
Gar I have found the easiest to catch during spawning season where they would move into the shallows. At this point you could honestly net one with little effort. When not in spawning season, fish 1-4ft of water. I used a nylon rope sewn at one end with a light jig head inside. The gars teeth would get entangle in the rope. I found the rope fairly easy to remove. If a few threads remain in the teeth, the gar will shake them off through time in the aquarium.