Reservations are accepted 4 months to the day of your first night's stay.
Baxter: (207) 723-5140, you'll want a site for two nights.
I recommend contacting the AT Lodge in Millinocket, they'll pick you up at the bus stop (7:45PM, over an hour from the Park gate), put you up overnight, and take you to Katahdin Stream Campground the next morning.
Sample itinerary:
Feb 5th, call BSP, book two sites at Katahdin Stream.
June 4th - Transportation day, the important connection to make is the bus from Bangor to Medway. Stay in town. Eat, pack shakedown, great hiker store.
June 5th - Shuttle in to the Park, check in with the Ranger, sign the first register, connect with other ATers, campfire with new best friends. Good night's sleep.
June 6th - Climb to Baxter Peak via the Hunt Trail. Pics at the sign, touch the cairn. Campfire and good night's sleep.
June 7th - Hike out to Abol Bridge on rested legs, last store til Monson, and head into the 100!

MEGA '17 guide to Baxter and Katahdin