The train connection from the airport to Centraal Station is excellent. Trains run every 15 minutes, it's cheap (6G) and fast (it should be - the airport is close to the city).
To get to places outside the city, you could take either buses or trains. I mostly rode my bike outside the city, and didn't use the buses at all. I used the trains for international journeys and for a few intercity journeys within The Netherlands.