dual pivot side pull brake shoe touches wheel rim. How do I fix it? Based on Sheldon Brown what I have on my front tire is the "Dual Pivot Sidepull" type brake. The right brake shoe touches the wheel without having to actually apply the brakes. The left has a small gap, and only touches the wheel when the brake is pulled as I would assume is expected behavior.

How exactly do I loosen it? Currently, I am riding on rollers, and I have rotated "up" the thingie (sorry I don't know the exact term . still learning the technical details) on the very left there, which has "loosened" the entire mechanism and now the brake shoes (obviously) do not touch the wheel rims anymore. But I can't really take it out on the road like this.

Which screws am I looking at loosening, or what exactly am I supposed to be doing to make sure the right brake shoe doesn't touch the wheel rim (while still being close enough to the rim that pulling on the brakes works correctly).
See at Sheldon's page about centering the brakes: meaning loosening the bolt that attaches the unit to the frame and rotating the caliper until both pads are at equal distance from the rim. Then re-tighten and check once more. You should also check if the wheel is correctly centered in the frame or fork. In case of doubt always refer to your LBS.