Tallinn University is the only university in Estonia that is accessible by tram. When coming from the city centre or Kadriorg, take either tram number 1 or 3 and get off at the Tallinna Ülikool (Tallinn University) tram stop.
It is also possible to reach Tallinn University by bus. It is easy to reach the university using bus routes numbered 1, 1A, 5, 8, 19, 29, 29A, 29B, 34A, 35, 38, 44, 51, 60, 63. When coming from the city centre, get off at the Uus-Sadama bus stop, and if you're coming from Pirita and/or Lasnamäe get off at the F. R. Kreutzwaldi bus stop.
Tallinn's public transport routes and schedules are available here.
Coming by car you will need to find a parking space in a public Pay-Parking area in the city centre or a Pay-Parking area near the university.