I can't really think of anything you need specifically for commuting, apart from maybe a pannier or practical small pack to carry everyday stuff in. But depending on your schedule, route and dedication you may be riding in heavier traffic, darker hours and worse weather than you're accustomed to. For that you'll need a visible jacket or vest - yellow is good, but reflective material is necessary in the dark - attentiongetting lights, and fenders if you'll be riding in the rain.
Depending on how far you're riding and the level of comfort you want, you can ride in regular clothes, stretchy warmup clothes, or go full out on cycling gear. I started off without, but I'd still definitely recommend at least 2 pairs of cycling shorts, and rotate them. Riding every day has a nasty way of bringing out saddle sores. If you're on a budget buy one pair of good shorts, and one cheapo to change around with.
Otherwise it's mostly a comfort thing. I'm lucky enough to have a shower at work plus I ride far enough that I most days need a shower once I get there, so I enjoy the comfort of riding in full bike gear from top to toe, and changing completely afterwards. In theory I could do the ride just fine in regular clothes, but this way I don't ever have to worry about grease stains or mud on my pants or sweaty tops, plus I almost never have to wash my office wear, just rotate my stash of tops and bottoms often enough that people don't notice 
Get out there and enjoy yourself! Explore new routes, you'll have a ball
Winter riding is much less about badassery and much more about bundle-uppery. - malkin
1995 Kona Cinder Cone commuterFrankenbike/Selle Italia SLR Lady Gel Flow
2008 white Nakamura Summit Custom mtb/Terry Falcon X
2000 Schwinn Fastback Comp road bike/Specialized Jett