A detailed description is reported of the analysis used by the CMS Collaboration in the search for the standard model Higgs boson in pp collisions at the LHC, which led to the observation of a new boson. The data sample corresponds to integrated luminosities up to 5.1 fb(-1) at root s = 7 TeV, and up to 5.3 fb(-1) at root s = 8 TeV. The results for five Higgs boson decay modes gamma gamma, ZZ, WW, tau tau, and bb, which show a combined local significance of 5 standard deviations near 125 GeV, are reviewed. A fit to the invariant mass of the two high resolution channels, gamma gamma and ZZ -> 4l, gives a mass estimate of 125.3 +/- 0.4 (stat.) +/- 0.5 (syst.) GeV. The measurements are interpreted in the context of the standard model Lagrangian for the scalar Higgs field interacting with fermions and vector bosons. The measured values of the corresponding couplings are compared to the standard model predictions. The hypothesis of custodial symmetry is tested through the measurement of the ratio of the couplings to the W and Z bosons. All the results are consistent, within their uncertainties, with the expectations for a standard model Higgs boson.