Under the Cuban Assets Control Regulations that have been part of the Trading with the Enemy Act since July 1963, you're perfectly free to go to Cuba, you just can't spend any money there. That said, the U.S. government has shown a pronounced lack of interest in enforcing the ban. The law specifies jail terms of up to ten years and fines of as much as $250,000 for individuals. During the last thirty years, though, the Treasury Department's Office of Foreign Assets Control (OFAC) has issued very few fines and only one person has gone to jail (he advertised fishing trips to Cuba and was jailed briefly in 1990).
There are some ways to go to Cuba and spend money legally--as a journalist, a government or business official, an academician, etc.--but they don't apply in most cases. To find out if you might qualify, contact the OFAC (phone 202-622-2480, fax 202-622-1657) or visit the U.S.-Cuba Trade and Economic Council's web page at http://www.cubatrade.org.
Otherwise, you can only do what every other American tourist has done and take your chances, preferably with one of the travel agencies that have been doing this for a while. Magna Holidays of Toronto (905-761-7330) offers luxury package tours to Havana and Varadero ranging from $650 to $1,100, including a week-long stay at a four- or five-star hotel, round-trip airfare and transfers. Aruba-based Last Frontier Expeditions, Inc. (303-530-9275), offers packages--including round-trip airfare from Cancún, a week in five-star accommodations, with meals, English-speaking guides and the chance to fish, play tennis and golf--for $1,300 to $1,600. You can also contact Cuba's own Havanatur, which schedules lots of Americans' trips (phone 011-53-7-23-97-90, fax 011-53-7-24-90-38).
You can, of course, go to Cuba without booking through a travel agency, but be aware that the direct flights from Canada and Mexico are often wildly overbooked--and that you'll need to have a tourist visa from the Cuban government before you turn up at Havana's airport. Remember, too, that this is one case when you can "leave home without it": For Americans, for now, Cuba is cash only. Which is yet another reason to pay a travel agent for as much of the trip as you can while you're still on our side of the border.