Competitive inhibition of an enzyme occurs at the orthosteric site. The inhibitor blocks the active site, preventing the endogenous substrate from binding and thus reducing the maximal rate (Vmax) of the reaction.
The binding efficiency of the substrate is not changed by the presence of a competitive inhibitor, however the number of enzymes available is impacted, as the inhibitor will prevent some / all from being available.
Mutational analysis is necessary to identify some types of inhibitors. This involves mutating residues within the active site of the enzyme, preventing the inhibitor from binding while still allowing substrate to bind and undergo the reaction.