From Barajas airport one can take a bus to Madrid, that stops right infront of the International arrivals lounge. This bus is fairly frequent (15-30 minutes periodicity) and its last stop is at Plaza de Colon, close to the town centre. If you continue to the University, you should go to that last stop, and locate the entrance to the train (Cercanias) station called Recoletos, also at Plaza de Colon. You can pick a train that takes you from that station to the University. There is also an underground (Metro) station at Madrid-Barajas airport that you can also take to go to downtown (See Metro Map here). If you bring heavy luggage, have in mind that you should have to change lines, and take stairs, quite often within the Metro network.
By TAXI
You can take a taxi from the airport to town for approximately 3000 ptas (20 dollars). If you are continuing to the Universidad Autonoma, perhaps the best choice is to ask the driver to take you to Chamartin train station, and take a train from there to the University. Obviously you might as well pick a taxi from the airport to the University, which would cost you around 4000 ptas.
By BUS
There are buses (# 714, 185 ptas.) from Madrid to the University, which are fairly frequent at typical peak hours. They leave from Plaza de Castilla (Terminal 13). You might reach Plaza de Castilla by metro (i.e., final stop for Linea 1). Then, exit the metro station and the bus terminals are just on the north side of Plaza de Castilla. The bus #714 to the University is the departing from the terminal closest to the metro station.
By TRAIN
Probably the best way. There is a train station
of the Renfe-Cercanias network at the University. There are
three lines that stop in "Cantoblanco Universidad", the official name
of the university station. The first two lines are called "Lineas C-7,
C-10" and they go from Madrid to Tres Cantos. Trains to Tres Cantos
(a small town north of Madrid) depart from Madrid South Train Station
called Atocha. The trains go underground along the Castellana
street. They stop at Recoletos (Plaza de Colon), Nuevos Ministerios
(close to the Consejo Superior de Investigaciones Cientificas) and
Chamartin station (the main North Train Station). After Chamartin, the
second stop on the way to TRES CANTOS is Cantoblanco-Universidad,
where you should exit.
The other Cercanias train line, which also stops at
Cantoblanco-Universidad is the "Línea C-1" and goes to
Alcobendas-S.S. de los Reyes ("ALCO-SSREY" will be shown on the
display), a residential area very close to the University. Trains of
this line can also be taken at the same stations than trains to Tres
Cantos.
In any case please always double checked the destination shown on the
display as trains to different destiantions depart from the same
platform.
The frequency of trains from/to Madrid to/from the university is about
every 5 minutes during rush hours. The trip to the University takes
between 15 and 25 minutes, depending on where you take the train. For
more information on the timetable of Renfe-Cercanias train network,
please look
here.