The Muon g-2 Experiment at Fermi National Accelerator Laboratory (FNAL) has measured the muon anomalous precession frequency ωam to an uncertainty of 434 parts per billion (ppb), statistical, and 56 ppb, systematic, with data collected in four storage ring configurations during its first physics run in 2018. When combined with a precision measurement of the magnetic field of the experiment's muon storage ring, the precession frequency measurement determines a muon magnetic anomaly of aμ(FNAL)=116 592 040(54)×10-11 (0.46 ppm). This article describes the multiple techniques employed in the reconstruction, analysis, and fitting of the data to measure the precession frequency. It also presents the averaging of the results from the 11 separate determinations of ωam, and the systematic uncertainties on the result.