First of, note that target tracking was done with radar systems from day one, long before ESAs came on the scene.
One way is to use monopulse tracking. In order to determine angle of arrival (AoA) of the returned signal in 2 axis, X & Y (or Az and El) your antenna needs to provide 3 outputs:
A SUM output, which is the normal output of an antenna.
A Delta-EL output, which is the difference between the upper and lower halves of the antenna, and
A Delta-AZ output, which is the difference between the left and right halves of the antenna.
The SUM output and the Delta-EL output are then processed in a complex (using amplitude and phase) fashion to determine the AoA of the signal in the vertical (Y) direction. Similarly, the SUM output and the Delta-Az output are processed to determine the AoA of the signal in the horizonal (X) direction.