We report the observation of electroweak single top quark production in 3.2fb⊃-1 of pp̄ collision data collected by the Collider Detector at Fermilab at √s=1.96TeV. Candidate events in the W+jets topology with a leptonically decaying W boson are classified as signal-like by four parallel analyses based on likelihood functions, matrix elements, neural networks, and boosted decision trees. These results are combined using a super discriminant analysis based on genetically evolved neural networks in order to improve the sensitivity. This combined result is further combined with that of a search for a single top quark signal in an orthogonal sample of events with missing transverse energy plus jets and no charged lepton. We observe a signal consistent with the standard model prediction but inconsistent with the background-only model by 5.0 standard deviations, with a median expected sensitivity in excess of 5.9 standard deviations. We measure a production cross section of 2.3-0.5+0.6(stat+sys)pb, extract the value of the Cabibbo-Kobayashi-Maskawa matrix element |Vtb|=0.91-0.11+0. 11(stat+sys)±0.07(theory), and set a lower limit |Vtb|>0.71 at the 95%C.L., assuming mt=175GeV/c2.