I'm looking for some advice on what structure to fish for them, what bait, and what techniques/presentations. I've caught some recently on shrimp but it hasn't produced much.

Thanks

Where are you fishing?

NE Florida or on the St.Johns River

If you don't own a cast net go buy one and learn to use it. If you do own one make sure you can use it, and then go catch you some legal baitfish. Shad would be best, but sunfish will work also. Cut them in pieces, maybe about silver dollar sized for smaller/mid size fish and if you want a big one use half a 6'' bait or more. In the river look for anything that breaks the current and put your bait at the front or tail end of it. Pay attention to bends in the river, will usually be a sandbar and a deep hole combo with those. Fish the sandbar where it drops into the hole. You can drift your bait or fish it one the bottom, blues don't always hold to the bottom like other catfish do. In the lake, look for creek channels, underwater points, and humps. Fish those by drifting or on the bottom. You may want to try shallow at nite, that can be fun.

My brother lives on a 50+ acre lake.   Years ago a pond above his lake had a dam break and all the catfish ran down a creek and into his lake. Since then catfish of 10-35lbs have been caught.  I never fished for them, but the other night I caught a small bream and rigged up a 3/4oz egg sinker, bead, hook and hooked the bream through the upper tail section and cast it out as far as I could and just stuck the handle of the rod in a fixture and left it and did some casting with a smaller set up. About 20 mins later the reel handle starts turning and line starts cranking off the reel.  Make a long story short I grab the rod and  set the hook and fought a big cat for 20+ minutes.  Did not get him, but I had a great time. The slime on my line was thick and went up about 3 1/2 feet!!!

Live bream is my bait from now on!!!

How did it come off?

I think that after 20+ min of the hook wallowing around and opening up a hole it just got the right angle and popped out. I was using a 5/0 wide gap bass hook. My next rig will be a circle hook.

Funny thing fighting that fish.  There were times when it felt like the fish was just sort of falling through the air with no resistance at all and then the slack would pop back taught.  My brother said that catfish will roll on you. I guess the line will roll around the fish and then when you pull and the fish is unrolling, that causes that sensation. I could also feel the line around his top barb. It would pop when it unhooked from the barb and tightened.  This was my first big cat and I learned a lot.

I have caught a 25 and a 45 pound carp. They pulled less than this big cat I had on. He was much stronger than the big carp.  My new cat rig will be heavier line and the circle hook.  I will need to get the fish up on the surface and closer to me a little faster.  I was only using 10 pound line and fought him too long.  

I was going to release it anyway, but I would have liked to have seen him.  Fighting a big fish in the dark I would have had to get him right up to the dock light to get a look and when I got him up close, I could not wrestle him up.  It stayed down deep.  I will get another chance.  

I used to fish for cats almost every weekend.  We fished the James river.  We found holes that had decent current yet had current breaks that ran as close to the dropoffs as possible.  We seldom used cut bait on blues bot opted instead to use live bait.  We also found that the bigger the bait the bigger the cat.  My best is about 45lbs but my cousin had a knack for catching the big ones and landed many 60+lb blues.  

Ive had great luck with cut baits.  Whatever you do stay away from store bought stink baits.  They are useless.  Around me in the midwest, a nice big golden roach on a circle hook works well too. 8-)

Live or cut bluegill were always tops for me when I used to fish cats a lot. Stinkbaits and chicken livers and such may catch some channels but don't work as well. If not fishing in real heavy current I like to use a large slip bobber sometimes referred to as a catfish pole float from 2 -5 feet off the bottom.

i caught a lot of cats in the Ohio river using cut bluegill, or i would take a minnow and step on to crush it. thats what i caught my biggest ones on.