By air as it is the quickest. We flew by helicopter from outside our hotel in Guardalavaca. The journey took 45 minutes as opposed to a bus journey lasting about 4 hours. For more information please see my Santiago De Cuba travelogue.
You can arrive to Santiago from Havana by plane... The fare is $100 one way, with both Cubana de Aviación or AeroCaribbean, and the flight takes 1 hour and 50 minutes. Another way from Havana is taking a Viazul bus... they are very comfortable, but the trip will last something like 16 hours ! Anyway there are night trips, so it will be not so bad. The price of the bus is $51 one way.
Timetables are quite variable, so... please ask to the various companies.
Someone told me: 'Train??? Forget it !!'
Getting around, the cheapest way is by 'carro particular' (private 'old' car)... otherwise also taxis can be not so expensive if taken in few people.
Airport Antonio Maceo has connections to Habana and Santo Domingo as regular flights, as well some charter flights.
Located in Juraguá beach, only 25 km away from the city centar.