When you dock at the location / station where you are to turn in your mission (delivery, collecting a reward for assassination), open the mission board, and the first item at the top of the list should be your mission...
Should be. There are some bugs that prevent you being able to turn in missions, the main ones are:
1. You were re-directed to a different target destination, in which case it is unlikely the mission will show up.
2. Part of the reward is cargo, but you have no cargo space on your ship.