Pressing GKEY activates Grab mode for all selected objects. These are now displayed as white wireframes and can be moved by using the mouse (without pressing any mouse button). To confirm the new position, click LMB or press ENTER; to cancel Grab mode, click RMB or press ESC. The distance of your movement is displayed in the header of your 3D Window.
You can lock movement to an axis of the global coordinate system. To do this, enter Grab mode, move the object roughly along the desired axis, and press MMB. Deactivate locking by pressing MMB again.
If you keep CTRL pressed while moving the object you will activate the snap mode and the object will move by an integer number of Blender units (grid squares). Snap mode ends when you release CTRL so be sure to confirm the position before releasing it.
If you are strifing for very fine and precise positioning you can try to keep SHIFT pressed. This way a large mouse movement reflects in a small object movement, hence allowing fine tuning.
An alternative way to enter Grab mode is to draw a straight line while holding down LMB. The location of selected objects can be reset to the default value by pressing ALT-G.