If I want to space the axle at 120...do I simply remove the nut, remove the spacer, adjust cones?
Yes, and if you're putting a single cog on there you also need to 'shift' the hub way over to the drive side to achieve a good chain line, meaning more spacers on the non-drive side of the hub than on the drive side. The wheel also needs to be dished.
'''96 Litespeed Catalyst, '05 Litespeed Firenze, '06 Litespeed Tuscany, '12 Surly Pacer, All are 3x8,9 or 10. It is hilly around here!
The following assumes you are using a quick release hub and skewer. If not, go back to your originally scheduled programming.
If the hub was originally 126 or 130 mm, you will have change to a shorter axle or shorten the stock one to assure the ends don't stick out beyond the frame's dropout faces and keep the qr skewer from tightening properly. A 120 mm hub normally uses a 131 mm axle and a longer one can be easily shortened with a hacksaw and the cut end filed smooth.