Not sure if you are seeking information on balancing or tuning of an antenna.
Balancing an antenna (or rather the transmission line) (taken from This post :
Unbalanced Lines. What happens when the currents on a transmission line are not equal? In the case of a parallel transmission line, the electromagnetic fields around the conductors will not be the same and will not cancel, so radiation from the transmission line occurs.
Thus, balancing an antenna system is not as important on a receiver as on a transmitter.
Tuning (impedance matching) of antenna to transmission line, and then to the receiver impedance (which I suspect you already know) is different from balancing.
I have an antenna tuner that I use. I simply adjust the antenna tuner to obtain maximum signal strength. Which of course doesn't guarantee an impedance match, but does the best I can with the limited resources.
Simple Tuner :
In your EDIT, you have focused in on "tuning".
Given that you might know your antenna impedance and receiver input impedance, a Smith Chart is very helpful and avoids mathematical calculations.
Plot the antenna impedance and receiver impedance on the chart. Then there are many many ways to use reactive components to transform impedance of one to the other.
Smith Chart Information describes Smith Chart better than I can.