Yellow Saddle's advice is good. You can just lever the tyre off one side of the rim where the nail is and pull out a section of the tube. Sand it and patch it in situ, then refit it and lever the tyre back on.
If you do want to remove the wheel, shift to the gear with the slackest cable tension. On my Alfine 8, that is 8th. I think Nexus is the opposite. Using a small allen key (I think it's a 2.5mm) as a lever in the hole on the cassette joint, rotate the cassette joint against the spring tension, and pop the cable end bolt out of its housing. Loosen the axle nuts and slip the wheel out of the dropouts. Gently slide the belt off to one side and the wheel will be out.
When refitting, bring the wheel back up and gently fit the belt from the side, then slide the axle back into the dropouts and tighten the axle nuts. Using the 2.5mm allen key again, lever the cassette joint against the spring, so you can put the cable end bolt back into its slot. Shift to 4th gear and check that the two yellow squares UNDERNEATH the cassette joint are lined up exactly.
It sounds worse than it is. I practised a few times at home, so that I will be okay out on the road.
(My bike has an eccentric BB for tensioning the belt, where yours has two bolts to move the axle back, but you shouldn't need to adjust the belt tension when remving the wheel).
Stroudy