We present a search for standard model Higgs boson production in association with a W boson in proton-antiproton collisions (pp̅→W[superscript ±]H→ℓνbb̅) at a center of mass energy of 1.96 TeV. The search employs data collected with the CDF II detector that correspond to an integrated luminosity of approximately 1.9  fb[superscript -1]. We select events consistent with a signature of a single charged lepton (e[superscript ±]/μ[superscript ±]), missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with a secondary vertex tagging method, a jet probability tagging method, and a neural network filter. We use kinematic information in an artificial neural network to improve discrimination between signal and background compared to previous analyses. The observed number of events and the neural network output distributions are consistent with the standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching fraction ranging from 1.2 to 1.1 pb or 7.5 to 102 times the standard model expectation for Higgs boson masses from 110 to 150  GeV/c[superscript 2], respectively. Academy of Finland Slovak R&D Agency Programa Consolider-Ingenio 2010, Spain Ministerio de Ciencia e Innovación, Spain Russian Foundation for Basic Research Institut National de Physique Nucleaire et Physique des Particules/CNRS Royal Society, United Kingdom Science and Technology Facilities Council, United Kingdom Korean Research Foundation Korean Science and Engineering Foundation Bundesministerium für Bildung und Forschung, Germany Alfred P. Sloan Foundation Swiss National Science Foundation National Science Council of the Republic of China Natural Sciences and Engineering Research Council of Canada Ministry of Education, Culture, Sports, Science and Technology of Japan Italian Istituto Nazionale di Fisica Nucleare National Science Foundation United States Department of Energy