Most probably you arrive at terminal North [Sever]. If you arrive at terminal 3 - South [jih], see paragraph below. Terminal 2 is used for flights from and to countries of Schengen Agreement, Terminal 1 for flights from and to all other countries. Terminal 3 is used mostly for non-public flights including charter flights. For details about the airport, see its web.
The dislocation of stops is drawn in the picture. To reach the City, bus 100 and trolleybus 59 (the shortest lines to Metro) are most suitable. To get to the Institute, you have to use bus 191 (in the peak hours, the bus leaves from the platform D of Terminal 1 and from platform B of Terminal 2 every 12-20 min, outside peak hours and on weekends every 20-40 min, at night bus 910 every 30 min - you possibly might travel to Větrník or Hvězda student dormitories near the Institute at night) and get off at the Sídliště Petřiny stop (19-23 min; 14th from Terminal 2 and 15th from Terminal 1) for the Institute.
Trolleybus 59 and buses 100, 191, and 910 depart from the stop on the main street (K letišti) approx. 200 m from the arrival hall. With bus No. 191, the Institute is at the 10th stop (14-15 min).
To get to city centre or to Academy residence Na Marně, you can use: