Cuba's national carrier is Cubana de Aviacion, connecting the island to a handful of destinations in Mexico, South and Central America, Canada and Europe. There are also regular holiday charter flights to resorts such as Varadero, and these can sometimes be less expensive than those going to Havana.
An official taxi to Havana central costs CUC25. There is a new bus service from the Terminal One (domestic flights) to La Habana Centro. So if you arrive in Cuba before 20:00 you can ask the taxi driver to bring you there and wait for the bus.
Astro is the bus line that most Cubans use. It has a much more extensive network than Viazul, and contrary to popular belief depending upon the vendor and your ability to speak Spanish, especially if your destination is not covered by Viazul, it is possible to purchase tickets.
There are also local provincial buses, consisting of overcrowded old beat-up eastern European buses that may or may not be running but they are very very cheap. Each town will have a "terminal terrestre" where buses or trucks serve local destinations and usually neighbouring provinces. They are usually quite easy to find - in La Habana it is found in the Lido, in the Marianao, whilst in Santiago it is found on Calle 4.
It is also possible to travel between some popular tourist destinations, such as Havana and Varadero, on special tourist minibuses carrying 4-5 people. The cost is a few dollars more but highly recommended if you are not planning to sleep the whole distance - plus you can ask the driver to stop along the way. Alternatively there are some collectivos which might acutally be cheaper than the official bus. The advantages of these collectivos is that they bring you exactly where you want, they can be cheaper and they run and stop for a snack when you want them to.
You will have to bring your own bike as bikes suitable for trekking are not readily available in Cuba. Make sure to bring all spare parts you might need along the way, since they will not be available in Cuba. Food for on the road can often be obtained locally for cheap Cuban Pesos, but make sure if you travel through more remote areas to carry enough food and water.
Car rental starts from CUC65 per day (including insurance) plus the cost of a full tank of gasoline. The refundable deposits start around CUC200. Rental cars are for the most part fairly new, imported European or Asian models.