  We present details on a new measurement of the muon magnetic anomaly, $a_\mu
= (g_\mu -2)/2$. The result is based on positive muon data taken at Fermilab's
Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses
$3.1$ GeV$/c$ polarized muons stored in a $7.1$-m-radius storage ring with a
$1.45$ T uniform magnetic field. The value of $ a_{\mu}$ is determined from the
measured difference between the muon spin precession frequency and its
cyclotron frequency. This difference is normalized to the strength of the
magnetic field, measured using Nuclear Magnetic Resonance (NMR). The ratio is
then corrected for small contributions from beam motion, beam dispersion, and
transient magnetic fields. We measure $a_\mu = 116 592 057 (25) \times
10^{-11}$ (0.21 ppm). This is the world's most precise measurement of this
quantity and represents a factor of $2.2$ improvement over our previous result
based on the 2018 dataset. In combination, the two datasets yield
$a_\mu(\text{FNAL}) = 116 592 055 (24) \times 10^{-11}$ (0.20 ppm). Combining
this with the measurements from Brookhaven National Laboratory for both
positive and negative muons, the new world average is $a_\mu$(exp) $ = 116 592
059 (22) \times 10^{-11}$ (0.19 ppm).
