Yes, the U.S. and Cuba have normalized diplomatic relations, but that doesn't mean you can pack your bags and book a flight to Havana. Only Congress can change the travel restriction, which is covered under the Cuba embargo law. Not the president.
Compare the revised 2012 travel guidelines listed by the U.S. Department of Treasury (which handles Cuba travel) to the new ones outlined Wednesday on the White House website: the restrictions are basically the same. You still need to apply to the feds for permission to go to Cuba. And unless you're a journalist, a government official, a businessman, a health or education worker, or you have close relatives in the country, that permission isn't going to be granted.
Since 2011, a few airports in the U.S. have been granted permission to host licensed charter flights to Cuba, which has made it easer for approved passengers to travel to Cuba. (American and JetBlue both operate charters.) After the announcement today, all U.S. international airports are eligible to service these charters, but they'll still need to apply for permission from the federal government. But U.S. airlines still can't initiate commercial routes to Cuba.
Still, if you really want to go to Cuba, there are ways to skirt the law. Cuba won’t stop you from entering, but you will get into trouble when you try to re-enter the U.S. with a Cuban passport stamp. To make sure that doesn't happen, you'll need to break another law—bribe the Cuban immigration officer to not stamp your book. Plenty of others have done it successfully: agencies that operate outside the U.S. have reported Americans make up to 20 percent of their business.