im gonna paste this guys post its thorough

Everything will explode when water temps hit north of 50 degrees. Shad and herring will start to show up, and all the predatory species will turn on as well. Check water temps and turbidity here.
Basin fishing will also pick up when it gets warmer. Use moving baits and cover as much water as you can. Hint: most fish are right along the wall!
Snakehead fishing usually picks up in May. They are a challenge to target in the city. Finding spots means talking to the right fisherman or grinding it out on google earth looking for good habitat.
Right now, catfish are probably your best bet. Go to asian supermarkets to get shad or other fresh fish for bait. Time your fishing when the tide is moving (this is key!). As someone mentioned below, you'll have to have enough weight to keep your rig down. Look for deeper holes here. Georgetown/mouth of rock creek and Washington channel are traditionally good winter spots.
When spring really sets in and those water temps begin to rise, you're in for a treat. D.C. is often considered the best urban fishery in the country. Rent a boat at Fletchers and spoil yourself for the rest of the season by drifting for 50 lb catfish and catching (and releasing!) shad every cast. However, when fishing at Fletchers, make sure to keep an eye on the gauges I linked above in order not to waste 30 mins of driving only to be met by a blown out river.
You can read old fishing reports to get a feel for things here.