The following points have direct bus and/or tram connection (without changing) to the Institute:

Tips for your orientation, if you never have been in
Prague:
The stops of trams and city buses are marked by bollards of red
and yellow colour with a symbol of tram (bus) in black, white and
blue. They are equipped with tables carrying a name of the stop
and line numbers. The stops are standardly equipped by time
tables of proper lines; time tables contain departures from the
stop, list of stops of the line with times to get there.
The direction is indicated on the front of bus/tram.
For more general information about Prague City Transport in
English language, see Prague
Information Service or Prague
Public Transit Company.
Take bus 179 (see a map of the airport). In the peak hours, the bus leaves every 12-20 min, outside peak hours and on weekends every 20-30 min. Get off at the Petřiny stop (14th stop from Terminal Sever 1, 13th from Terminal Sever 2; 8km, 19-23 min), then walk 100 m back. An Institute building is located behind the tram terminus. (see a map or a commented photo)
Take the Metro (red line C) in direction of Letnany (indicated
at entrance to the Metro station) to the Vltavska station (see
a map) (2 stops)
and change for tram 1 to in
direction of Petřiny to its last stop (7 km, 21-22 min), after
getting off continue forward approx. 50 m to the Institute
building.
Another variant:Take the Metro, red line
C (direction of Haje) to the Muzeum station (1 stop, 1 min)
and change for green line A (direction of Dejvicka) to the
Hradcanska station (4 stops, 7 min). (a map)
Then take tram line 1 or 18 as far as Petřiny
(terminal; 5 km, 13 min).
Take the Metro (red line C, direction of Haje) to the Vltavska
station (1 stop, 4 min) (see a map)
and change for tram 1 in
direction of Petřiny to its last stop (7 km, 21-22 min).
(see a map)Take the Metro, the red line C
(direction of Letnany) to the Vltavska Station (2 stops, 4 min) (see
a map)
and change for tram 1 to
Petřiny (last stop; 7 km, 21-22 min).
Other variants:
Take tram 26 (direction of Liboc, Divoka Sarka) to the 8th
stop - Hradčanská (4 km, 13-15 min ), (see a map)
change for tram 1 or 18 to Petřiny (terminus, 5
km, 13 min)
Other variants:
Take the Metro, the yellow line B (direction of Zlicin) to
Nove Butovice station (3 stops; 8 min), (see a map)
then use bus line 179
to 11th stop - Petřiny (7 km, 14-18 min). The stop of bus 179 is
located directly in front of the Institute. Before the stop, the
bus passes a tram terminus, what can help you to recognize the
correct stop to get out.
Another variant: Take the Metro, yellow
line B (direction of Černý Most) to Anděl station (1 station;
2 min) or any tram (4, 12, 14, 20) to Na Knížecí stop
(2 stops) , (see a map)
then use bus line 191 to Petřiny (terminal; 10
km; 19-22 min).
Take tram line 1,18 from the stop Hradcanska or 2 from the stop Vitezne namesti to Petřiny (5 km, 3 min)
Use direct bus line 191 to Petřiny (10 km, 19-22 min).
Take the Metro, line A (direction of Dejvicka) to Hradcanska
station (8 stops, 14 min)
and change for tram line 1, 18 to Petřiny (last
stop, 5 km, 13 min).
Take bus line 160, 355, or 359 to its terminal stop Dejvicka (see a map), then take tram 2 to Petřiny.