Bergamo is a pretty town of some 120,000 people nestling in the foothills of the Alps. Widely acclaimed as a city of rare beauty, Bergamo is famous for its wealth of artistic treasures and enchanting medieval atmosphere. It is a real life tale of two cities: “Città Bassa”, the busy and modern lower city, and "Città Alta", the upper city with its rich heritage of art and history.
Bergamo is the location of the Orio al Serio International Airport  (BGY) (Phone number: +39035326323), an airport oriented around low-cost airlines (Discount_airlines_in_Europe). ATB no.1 bus to the city are € 1.70 per trip, € 3.50 for 24h ticket and € 5.00 for a 3 day ticket. There is a ticket machine at the bus stop. You can find schedules and route maps on the site of ATB  the local mass transit authority.
Cabs will take about 15mins but are quite expensive given the length of the journey - cost around €15 (€21 after 21:00 in the evening)
Note that buses can be both unreliable and not punctual. You'd better take the no.1 city bus 30 or 45 minutes before the time you actually have to be at the airport.
Milan is about 30-40 minutes away by train. There is no train station at the airport in Bergamo. The 1-airport bus to Bergamo city, taking around 30 minutes, leaves you just in front of the train station. From Bergamo city regular trains to Milan, Lecco and Brescia, on to Verona and Venice. You can check schedules and fares on the website of the Italian Railways . There is no left luggage office at the train station, only at the airport. If you are at the airport and your destination is Milan or Venice, just take one of the regular coaches. However be warned that the autostrada connecting Bergamo and Milan carries a lot of trucks and gets easily congested - do not therefore rely on the 'stated' journey time especially on weekdays. An alternative is to take the bus into Bergamo (see above) and take the train, which is cheaper and quicker.
Regular buses to Milan. You can check schedules and fares on the website of Autostradale . The trip takes approximately one hour, depending on traffic conditions. The bus stop in Bergamo is located near the train station and there is a counter where inquiries can be made.
The town is not large, and most of the sights can be seen comfortably on foot. To get from the Città Bassa up to the Città Alta can be quite tiring on foot, though, due to the steep and winding streets, but there is a funicolare (a kind of tram) linking the two parts of the town. You can see a map of bus routes, schedules and fares on the website of the local mass transit authority  (in Italian). The ticket that you purchase for the funicular is valid for 75 minutes and you can reuse the same ticket for travel on the bus as well as the funicular to San Vigilio. Walking from the train station to the Città Alta funicular station is pleasant and takes about 20-30 minutes. You can also walk from Città Alta to San Vigilio instead of taking the funicular, which will afford you great views of the surrounding areas, as well as the quaint narrow streets and houses along the way.
For snacks, a drink or simply the great view, Cafe Funicolare in the city Alta Funicolare station. For lunch or an evening meal try Da Franco Ristorante Pizzeria Via Colleoni 8 Bergamo Alta Telefono 035238565 - closed Mondays or Da Mimmo  - closed Tuesdays - both more than just a Pizzeria. Also worth a look is Il Sole, on the corner of Piazza Vecchia and Via Colleoni. La Bruschetta, in the Citta Bassa, just off Porta Nuova is a good value restaurant/pizzeria in the cellar of a building and worth a mention. Also in the Citta Bassa area "La Ciotola" is a good restaurant/pizzeria near the Mercure hotel. For great ice cream try La Siesta  on Via Sant'Alessandro.
There are a number of good hotels in the new town (Citta Bassa) - many on Viale Papa Giovanni XXIII (The main street from the station to the funicolare)
Other places of interest around Bergamo