It looks like we have a lot to read on the new Cuban Travel Regulations. Most of the current regulations come from the Treasury Department's Office of Foreign Assets Control. On March 11th they issued a General Guidance on Implementation of the Bill that was passed and a general license for visits to close relatives. This authorized persons subject to the jurisdiction of the United States to travel to Cuba to visit close relatives for an unlimited period of time once every 12 months and to engage in travel-related transactions. OFAC action on Cuba Travel
On March 13th the President issued a Presidential Memorandum eliminating all remaining restrictions on travel, remittances and gift parcels to Cuba for people who have relatives on the island.
There is still a list of Authorized Cuba Travel Service Providers and all visitors must hold a valid passport. U.S. citizens will require a visa unless born in Cuba, in which case a Cuban passport is required.
While current regulations only allow travelers with family members on the island, the president's memorandum allows U.S. telecommunications companies to obtain licenses to operate in Cuba. The Freedom to Travel to Cuba Act introduced in February by the House of Representatives would remove travel restrictions on all Americans and U.S. residents. There is also a bill in congress and while the bills have bipartisan sponsors, it isn't clear whether they will come up for a vote anytime soon.