The Marti International Airport is about 25km from the capital city of Havana and is where nearly all international flights will come in to. The national carrier from Cuba is Cubana de Aviacion. They offer domestic and international flights to the rest of the world.
Taxis to and from the airport cost around 25 CUC. There is a bus service that will take you into La Habana Centro for just a few cents, but it only departs from the domestic terminal (terminal 1). You could get a taxi to take you from the international terminal to the domestic and then get the bus, if you're really looking to save some money.
Viazul is the most prevalent tourist bus company in Cuba. They have a good reputation for being the best mode of long-distance transport. Coaches have TVs and restrooms and are comfortably air-conditioned. They're also reliable and usually on time. Bring your own food on board for the long distances. You can travel to most of the big cities in Cuba by bus enjoying the scenery as you go.
Astro buses are the cheaper option and so used by Cubans. Boarding an Astro can make for a great experience if you've got plenty of time. Make sure you account for the fact that they often break down and buying your ticket is never as easy. Another option, for just a few extra dollars, is to use the minibus service that carries 4-5 people between popular tourist towns. If you're backpacking through Cuba with a group of mates this is always a good choice.
The trains in Cuba can be unreliable. The service is old and irregular, but boarding a train in Cuba is an absolute must. You can get an overnight service from Havana to Santiago de Cuba most nights of the week. If you're in Cuba and have some time on your hands this is a great idea as there is much more to Cuba than just the capital.
It's perfectly normal to split the price of a taxi among others going your way in Cuba, even if they are strangers. If you're travelling a long distance sharing the fare can work out the same price as a bus or a train.
Cars drive on the right in Cuba. Car rental costs between 50-70CUC per day. Be wary if you're renting a car in Cuba, like anywhere. Make sure you check the car over beforehand and point out and photograph any dents or problems. Make sure the seatbelts, lights and doors all work. You should always pay the extra for insurance too. And just a word of warning; if you have a traffic accident involving serious injury or death, you may be detained by the Cuban government until the legal process is resolved.