Coming to Oxford from abroad, the best options are:
This is usually the best option for those flying long distance. There is an excellent direct bus service to Oxford (tell the driver you want to go to Gloucester Green bus station -- "Gloucester" is pronounced "gloster") with 2-3 buses per hour taking 80-90 minutes from the Heathrow Central Bus Station (Terminals 1-3) and Terminal 5. Those flying into Terminal 4 must first take either an underground train to the Central Bus Station, or a local bus 482 or 490 to Terminal 5 -- the bus is usually slightly faster.
This is a good option for European flights -- I prefer Birmingham to Heathrow because it is a much smaller airport. There is a regular train service to Oxford from the adjacent Birmingham International station. There is usually one train per hour, and they take about an hour. There is also a new (2016) bus service to Oxford, but it takes 2 hours.
Other options are:
Once you get to Oxford, the map on page 3 of this PDF shows the location of the bus station (blue bus symbol) and train station (red train symbol) and all of the colleges and departments within the university.
If you come to the bus station, there are taxis available on the East side of Gloucester Green, near the junction with George Street. For those coming to the train station, there are taxis immediately outside.
Additional information is available from: