If you turn off the M1 at the junction for the airport, follow the dual carriage way underneath the approach, you will see a layby on the opposite side. Carry on to the roundabout and turn 180 (as if you are going back to the M1) and park in the layby. You can then walk 100m approx, and you will be able to take photographs of landing aircraft.
The best place for seeing "what is going off" is at the opposite end of the runway and to the north. To get there, follow the signs to the Donnington Park, pass the airport and and you come to a set of Traffic Lights. Turn right and ignore the Donnington Park signs on your left. You are now motoring past the western end of the runway. At the roundabout, you can go straight on and park near the Aeropark . A better thing to do is to turn left at the roundabout (you are travelling towards Castle Donnington) and after a few hundred metres turn right at the side of the Nags Head Pub. Follow this road to a crash gate parking sensibly. This is where all the locals go. You can see across to Cargo West and Terminal, not very good views of Cargo east. You will see all arr/dep. Disadvantage - you are facing south so photography is difficult up to 4pm.
Hope this is useful.