We present an overview of the muon reconstruction and identification methods employed by the DO collaboration to analyze the Run II (2001-2011) p (p) over bar data of the Fermilab Tevatron collider at root s = 1.96 TeV. We discuss the performance of these methods, how it is measured using DO data, and how it is properly modeled by the DO simulation program. In its pseudorapidity acceptance, vertical bar eta vertical bar < 2, the muon system identifies high-p(T) muons (p(T) greater than or similar to 10 GeV) with efficiencies ranging from 72% to 89%. Muons tracks are reconstructed in the DO central tracking system with efficiencies ranging from 85% to 92% and with a typical relative momentum resolution of 10% for p(T) = 40 GeV. Isolation criteria reject multijet background with efficiencies of 87-99%.