The usual meeting place is the Ranger's workshop ("Estovers") at grid ref SU 500 652.
Greenham Common is about 3 km southeast of the centre of Newbury.
The main car parking area is off a roundabout (grid ref SU 499 652) on Bury's Bank Road. If you're coming from the west this is a few hundred metres past the Golf Club entrance, or coming from the east it's a few hundred metres beyond the second cattle grid.
Coming from the roundabout onto the common, the track straight ahead is signed for the main (Control Tower) car park. Don't take this, but instead go sharp left on a gravel track towards two metal-clad warehouse-style buildings. Pass the near one, on your right, and go to the further one. This is the workshop.