From Bremen Airport, there is a direct coach service to Oldenburg - Public Express. There are stops in Oldenburg at the Hauptbahnhof, Pferdemarkt and the university.
Alternatively, catch tram 6 from the airport to Bremen Hauptbahnhof, then catch a train.
At the airport, it is also possible to take a taxi to Oldenburg.
There are usually two or three connections per hour from Oldenburg to Bremen operated by Deutsche Bahn and Nordwestbahn (Tickets are valid in the trains of both companies). The fastest train takes 28 minutes, the S-Bahn trains take up to 38 minutes. The fare is around 8€ for a regional train (NWB and RE), for IC and ICE trains a supplement is neccessary. Other regional services are linking Oldenburg with Wilhelmshaven (for the ferry to Helgoland), Emden (ferry to Borkum), Norddeich Mole (ferries to Norderney and Juist), Osnabrück and Leer. The trains are usually running every 60 minutes and every 30 minutes during peak hour. See the Deutsche Bahn online timetable for details.
ICE high-speed trains and IC long distance trains operated by Deutsche Bahn are running e.g. to Munich, Leipzig, Dresden and Berlin.
You could also travel from Groningen. You'd then take the train to Leer (D) and from there on to Oldenburg. Be aware of the border crossing after Nieuweschans. You can't use a dutch ticket to go to Germany.
You can reach Oldenburg from the A1, A7, A27 and E22 highway.
The central station and the city centre can be easily explored as pedestrian. For longer distances there are Bus services to all parts of the town. The main interchage stations are Lappan and ZOB (central station). Getting around by bike or car is easy. For parking in the city centre you should follwow the signs to one of the several parking garages.
Carl von Ossietzky University (founded 1973) is an important regional university.
There are a host of eateries in the city center, including a variety of doener stands, Chinese Food, a McDonalds and a Burger King for the cash-strapped college student. On weekdays the Pferdemarkt hosts a market at which you can buy fresh baked breads, vegetables, and meats.
There is a good selection of small cozy places in Wallstrasse.