First, bike must be upright. I sometimes see people remove and install wheels with the bike up side down. I don't understand this concept.

Assuming this is a bike with trackends or horizontal dropouts, whether it's fixed, single speed, or geared makes no difference.
Bike must be upright. Place one hand between the wheel and seat stay to push back and center the wheel while tightening the axle nuts with the other free hand. That's it. This shouldn't take longer than a few seconds at most.