A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, H→cc[over ¯], produced in association with a leptonically decaying V (W or Z) boson is presented. The search is performed with proton-proton collisions at sqrt[s]=13 TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb^{-1}. Novel charm jet identification and analysis methods using machine learning techniques are employed. The analysis is validated by searching for Z→cc[over ¯] in VZ events, leading to its first observation at a hadron collider with a significance of 5.7 standard deviations. The observed (expected) upper limit on σ(VH)B(H→cc[over ¯]) is 0.94 (0.50_{-0.15}^{+0.22})pb at 95% confidence level (C.L.), corresponding to 14 (7.6_{-2.3}^{+3.4}) times the standard model prediction. For the Higgs-charm Yukawa coupling modifier, κ_{c}, the observed (expected) 95% C.L. interval is 1.1<|κ_{c}|<5.5 (|κ_{c}|<3.4), the most stringent constraint to date.