Pick the right time of year. Storms that drive you off course or do damage to the boat are your number one enemy in an Atlantic crossing. Hurricane season in the Atlantic lasts from early summer to the last storms of early winter. Plan a time that is hurricane-free and as warm as possible for your trip.
Know your boat. There's a big difference between a bay-cruising boat and a boat that can withstand the tests of the Atlantic. Make sure both the boat you sail on and the crew you sail with are up to the challenge. Speaking with the skipper of the boat is a good way to start.
Join a rally. Rallies are convoys of boats that cross a large body of water in a semi-competitive, and sometimes very competitive, way. The Atlantic Rally for Cruisers is one of the best-known Atlantic rallies that is open to cruising boats. Check out different rallies to find one that suits your situation.
Be prepared. Getting yourself prepared doesn't simply mean going through the checklist of gears and things to do, however important those things are. Crossing the Atlantic is a long process in which anything can happen. It's important to be as prepared for long stretches of windless boredom as it is for violent storms. The better you handle things as they arise, the more pleasant the journey will be.