As far as balancing a wheel, we start by considering the design parameters. Our 26" bicycle wheel goes .077 mph per rpm, so at 50mph it is doing 650rpm. At this rotational speed, balance may be an issue if the components are not the same weight all around even if the wheel is perfectly round. Due to relatively precise manufacturing tolerances, we'll assume that the parts of the wheel are the same weight all around. After truing, a wheel may still be slightly out of balance weight wise, and we can either fix this by adding weight in the right places, or just let it go as it will not be noticeable anyway. On cars this is a larger issue, as the wheels are sometimes smaller and must turn much higher rpms, so weight balance is a real issue.
So the logical way to balance a wheel is to make sure each part is the same distance from the center. Start by loosening all spokes and then hand tightening them to the same amount. Give the wheel a spin watching for radial trueness. Adjust as necessary until the spokes are the correct tension (see my thread link; spokes can be tensioned roughly to a pitch that depends on their length). From there true horizontally and dish the wheel if needed. But not too much! Properly dished wheels use different length spokes for right/left, but for our purposes running single speed we don't really care.
To make adjustments: radial: tighten groups of spokes both sides a quarter turn, then loosen spokes on the 180deg around side side the same amount. Very tedious ; usually better to start with a rim that is true.
Horizontal: tighten spokes on one side the same amount that spokes on the other side are loosened.
A rim that is out of true as stock should be replaced, but sometimes you can get away with truing it to shape. You can always reuse your old spokes. Easy way to do this is to zip tie crossing spokes, then remove nipples and replace the rim.
When loosening spokes, turn it farther back than you want to loosen, then tighten back up to the new setting.
The important next step is to stress relieve the spokes. This is done by squeezing together crossing spokes, going around the wheel. This step subjects pairs of spokes to a much higher tension than they would undergo in use, and they settle back to their tensioned state with miles to go before reaching their yield strength.
Ride the wheel maybe 20-40 miles, then true and stress relieve again. DONE!
I balance radially to within .010". Once I trued a rim with the zip-tie guide, then threw the dial indicator on there just for kicks. I was within about .005" side to side! The indicator has not seen another wheel.
Link to my 48 spoke rear wheel riding on a 36h drum hub. Link to spoke tension pitches is in there.