We study the indirect effects of new physics on the phenomenology of the recently discovered "Higgs-like" particle. In a model-independent framework these effects can be parametrized in terms of an effective Lagrangian at the electroweak scale. In a theory in which the S U ( 2 ) L × U ( 1 ) Y gauge symmetry is linearly realized they appear at lowest order as dimension-six operators, containing all the standard model fields including the light scalar doublet, with unknown coefficients. We discuss the choice of operator basis which allows us to make better use of all the available data to determine the coefficients of the new operators. We illustrate our present knowledge of those by performing a global five-parameter fit to the existing data which allows simultaneous determination of the Higgs couplings to gluons, electroweak gauge bosons, bottom quarks, and tau leptons. We find that for all scenarios considered the standard model predictions for each individual Higgs coupling and observable are within the corresponding 90% C.L. allowed range, the only exception being the Higgs branching ratio into two photons for the scenario with standard couplings of the Higgs to fermions. We finish by commenting on the implications of the results for unitarity of processes at higher energies.