Nick, welcome to the addiction. I generally use a 6 wt with a reel with a good drag. I chase them in clear water for the most part, so I use a 12' with the last 3-4' being 3x fluorocarbon. You can go shorter in less clear conditions. Nymphs, wooly buggers (carp love crayfish if they're present in your waters) and egg/sucker spawn flies will all work.I would also never be without carp worms/San Juan worms with a beadhead or small beadchain in red, pink and chartreuse. I generally tie on 2x strong/heavy nymph hooks- they will straighten light trout fly hooks. Look for fish feeding, rather than cruising. Polarized sunglasses are a great help. You can spot fish tailing, or in murky water look for bubble trails (carp rooting in the sediment releasing methane bubbles) or discoloration from the surrounding water called "muds". If you can determine the direction or orientation of the carp, cast slightly ahead and to the side . I wait maybe 5 to 10 seconds and give the fly a slight twitch if I see or feel no response. Keep your line taught as carp are very quick at rejecting flies. If you can see them tilt up on your fly, strike! If you're fishing blind, strike at the first sign of tension. Flies with beadchain that ride hook-up are excellent, as they snag much less. Small Clousers can be effective, too- carp will eat minnows. One of the largest carp I've ever seen was busting a school of yellow perch! I've caught several over 20 lbs. using clousers in the 3-4 inch range. Not the norm, though. Carp are not overly fast swimmers and they'll roll rather than jump. Keep pressure on them, change directions of pull to confuse them, keep your rod tip down and let them tire themselves out running against the drag and fighting the rod butt. A large net is handy, though you can carefully beach them. Don't use a lipping device like a boga-grip- it'll do damage. There's many different scenarios and foods carp love - they truly are omnivorous- I could write pages and pages of what's worked at times. Get started and you'll learn a ton as you go. One more tip- carp are very cautious and have many defense mechanisms. They release pheromones when they get frightened to warn other carp out of the area. Lots of times, they are the apex predator in a body of water and will move off slowly when they've figured out you're there. They will NOT feed and you'll have to move on or wait them out. Move slowly and cautiously. It's as much hunting as fishing. An absolute blast.
I fish north of Beantown in the salt quite a bit. I've seen some monsters in the Merrimack and I've heard the same for the Charles. I'm concentrating on stripers, so I've only caught a few near the coast.