If you come from abroad, Groningen can be most easily reached by flying to Amsterdam (Schiphol airport), then taking a direct train from the airport to Groningen (2.5 hours). The train station is located directly underneath the airport.
Alternatively, you may fly to Bremen airport (Germany) from where there is a direct bus connection to Groningen central station. The bus also takes about 2.5 hours to reach Groningen.
The university is located in the town center which is within walking distance of the train station (about 10-15 minutes).
Information about things to see and do in Groningen can be found on the website of the city of Groningen.