Arriving by air: Bergamo has its own airport (Orio al Serio - airport code: BGY), mostly used by low cost carriers -- which generally sell it as it were a Milan airport (it is not). The airport website www.sacbo.it has complete information on flights, connections to Bergamo and Milan, etc.
In the event you arrive at one of the 'real' Milan airports (Malpensa - MXP - or Linate -LIN) and need to proceed to Bergamo, you will first need to reach Milan and proceed by train or bus from there.
Arriving by train: Bergamo is on the main Trenitalia network, and has direct connections with Milan, Brescia (change there for Lake Garda and Venice), and Lecco (on the E shore of Lake Como). There also is one daily direct Eurostar link with Rome, and one daily direct connection with La Spezia (for the Cinque Terre) and Pisa. Besides, Bergamo is connected with every major Italian destination, usually changing trains in Milan. See www.trenitalia.com for complete schedules.
Arriving by bus: Buses are another cheap and efficient way of arriving to or departing from Bergamo. There are direct bus links from Milan (http://www.nordesttrasporti.it/Tabell... to reach the city of Bergamo, http://www.autostradale.com/ to reach the Bergamo airport from Milan or Brescia) and Como (http://www.asfautolinee.it/LinkClick....US). Bus timetables for the province of Bergamo are available at www.bergamotrasporti.it