Birmingham International railway station is directly linked to the airport passenger Terminal by SkyRail - when arriving go towards Birmingham International and the NEC, this will bring you to the SkyRail (you will need to go up a level from the ground level arrival hall). The SkyRail is free, operates about every 2 minutes when the rail station is open and the journey takes less than 2 minutes. This "tutorial" shows a few images of the way to the Airport to the railway.
To get to Birmingham city centre it is a 10-15 minute journey from Birmingham International rail station to Birmingham New Street station. There are 6-7 trains running an hour during the day, less frequently in the evenings and at the weekend and no trains during the night. Go to the Venue page to see how to get from New Street Station to the Venue and Birmingham University.
If you want to travel by taxi you should not use the SkyRail described above - most taxies are located outside the ground level of Terminal 1 (this is where you arrive). The drive to the city centre from Birmingham Airport takes around 30 minutes, depending on traffic. The price for a saloon car is typically around £25-£35 to the city centre. Note that most taxies only accept cash payment; taxies from T.O.A. should accept credit card payment. You can find more info on travelling by taxi from the airport here.