Passports and visas
A valid passport (with a minimum of 6 months validity after your return date) is required for entry into Cuba. In addition, you are required to show your passport at all accommodations even casas particulares.
A Cuban tourist card/visa* is required for entry into Cuba. The visa comes in two parts so it is important that you keep your tourist visa in a safe place, as it will be necessary to give the remaining half upon departure from Cuba.
This is not in any way related to legal categories of travel to Cuba for Americans since the visa is a requirement from the Cuban government and the legal categories are a requirement from the US government.