Travel to Cuba is only restricted for anyone under U.S. jurisdiction, and non-Cuban citizens who were born in Cuba. The latter group must apply for a visa at a Cuban embassy. Those under U.S. jurisdiction are technically allowed to travel to Cuba; however, it is illegal to make any transactions, unless they have a license.
Exceptions are made for journalists, government officials, full-time professionals and those with relatives in Cuba. If you fall into one of these categories, you can qualify for a "general" license. Exceptions are sometimes also made for humanitarians, researchers, students participating in a formal study program, those traveling for religious activities, artists and athletes.
You have to apply for a general or specific license before traveling to Cuba. You also need a passport as well as a tourist card, which is issued with your plane ticket.