The Fermilab Muon $g-2$ Experiment was designed to measure the muon's anomalous magnetic moment $a_{\mu} = (g-2)/2$ to 140 parts per billion. The value of $a_{\mu}$ is proportional to the difference frequency $\omega_a=\omega_s-\omega_c$ between the muon's cyclotron frequency and spin precession frequency in the uniform magnetic field of the $g-2$ storage ring. The frequency $\omega_a$ is extracted from the time distribution of the mu-decay positrons recorded by 24 electromagnetic calorimeters positioned around the inner circumference of the storage ring. We will discuss the various approaches to the frequency determination including the reconstruction, fitting of time distributions, and procedures for handling the effects of gain changes, positron pileup and beam dynamics. We also discuss the data consistency checks and the strategy for the averaging of $\omega_a$ across the different analyses.