You'll need gloves that allow you to still hold the bars and use the brakes and shifters. Standard mittens don't work well since you have to grab the brake with all your fingers.
Durable waterproof ski gloves with five fingers are one of the best options, especially those which come with a hand warmer pocket for extra warmth capability. Some folks prefer lobster style gloves since they are split and allow you to wrap two fingers around the bars and two on the brake on a flat bar setup. They still suffer a bit when using STI shifters, but they are usable.
Gloves that have a separate outer an inner layer are very helpful for longer duration riding as you can keep a set of dry liners handy to swap out if your hands sweat a lot, since moisture will transfer cold from the liner to your fingers. I've found this a lifesaver on long rides where my hands begin to freeze up. If using on commutes, it's nice to have separate liners for to and from trips, in case your liners don't dry through the day.
For extra cold conditions, a lot of people prefer to combine thinner gloves with pogies / bar mitts. These provide a lot of wind shielding as well as some insulation, enabling you to forgo super heavy gloves. They are available for both drop bar and flat bar setups, but they are more optimal on flat bars.
Some popular brands of gloves to check out are:
45nrth - See Sturmfist gloves (some of the best deep winter cycling gear)
Pearl Izumi - See Pro Softshell Lobster Glove (one peice, makes layering hard)
Planet Bike - See Borealis Glove (lobster style, separate liner)
Swany - See X-change Gloves (some of the best ski gloves, also awesome for winter cycling)
45nrth Cobrafist (Flat bar only)
Revelate Designs (flat bars and jones loop bar compatible models)
Dogwood Designs Pogies (Flat bar only)
Barmitts (Both Flag bar and drop bar models, simple neoprene design)
AMF Threadworms Moose Mitts (Drop bar and flat bar models available)