Since we started out our journey from NYC, there was no way getting directly to Cuba. Due to the US embargo, there are no direct flights available. We chose a flight via Cancun (JetBlue and Cubana). Another popular route is via Toronto.
You need an entry permit, which you can apply for online (link). Seems largely a way to make money, rather than a true check.
Notice that Cuban authorities will not stamp your passport. Some brave US citizens use that to sneak into Cuba despite the US ban.
Flying Cubana from Mexico was a bit of an adventure. The boarding procedure is not the typical one: Forget the one personal item constraints. Everyone brings as much as she or he can carry....