In the Netherlands, cars drive on the right side and speed limits are in place both within (30 or 50 km/h) and outside (80/100/120/130 km/h) of urban areas.
Important exit roads in and around Nijmegen are: the A325 (connecting Arnhem and Nijmegen), the A50 (Apeldoorn-Eindhoven), the A73 (Maastricht-Nijmegen) and the A15 (Rotterdam-Nijmegen).
In Nijmegen there are two main traffic plazas, of which the Keizer Karelplein is the most wel-known one. On both plazas (Keizer Karelplein and Takenhofplein), traffic coming from the right has priority, also over traffic already on the roundabout. Therefore, always allow traffic coming from the right to go first. A complicating factor is that there are no lines indicating lanes: you can theoretically drive wherever you want. In practice, the further the exit you are taking, the more you are expected to stick to the left side (the middle of the roundabout).
As an extra caution: always be aware of cyclists, who sometimes tend to take their privileged position in traffic somewhat too liberally. Keep in mind that cyclists are allowed to pass you on the right side (where there will often be a bicycle lane anyway). Leave room for cyclists to your right and take care when turning right – bikes have the right of way when going straight.