We mostly have fished for catfish at Fletcher’s Cove in northwest Washington, DC in the morning—say, 8am to 11am. Channel catfish are native and worth returning to the river. Blue catfish are invasive, and the fish and game authorities recommend killing them.
Shore fishing for catfish is doable, but it is much better to get into the center of the channel or under shade (bridges and trees). Catfishing is bottom fishing. Get the sinker to the bottom and have the bait flapping a foot or more up.
All catfish caught were 12-24 inches, with some river monsters snapping lines. (I had 12 pound test broken very fast by one.)
The rig that has worked best for us is a 1 ounce, pyramid weight (more or less depending on the current) at the end of the line (Hangman’s Knot—to allow it to break away if it gets snagged without losing your hook and everything above. Use a Palomar Knot if you are feeling tired or confident you won’t snag.) About 12-16” up from the sinker, fold the line and tie a 5 Twist Simple Knot to create a 6”-10” long doubled-line.
At the end of that doubled line use a Catfish hook or treble hook pre-loaded with a chunk of hot dog, and simply slip the line through the hook eye and loop it over the hook to fasten it. (Alternatively, you can use a wire catfish rig, which comes with easy clips for the sinker and hook.)
Do use a net to haul up the catfish—we had two or three snap the line right at the end of the boat.
7/26/2014 update: Guys near us caught a 36” catfish that was hugely fat on blue gill. He was using 50-pound test line (possibly braided?). I brought in a 30” catfish on my 12-pound test. It bit on beef hot dog, as did the 20” and 15” catfish I caught that same day.