This thesis discusses in detail the measurement of the polarizations of all S-wave vector quarkonium states in LHC proton-proton collisions with the CMS detector. Heavy quarkonium states constitute an ideal laboratory to study non-perturbative effects of quantum chromodynamics and to understand how quarks bind into hadrons. The experimental results are interpreted through an original phenomenological approach, which leads to a coherent picture of quarkonium production cross sections and polarizations within a simple model, dominated by one single color-octet production mechanism. These findings provide new insights into the dynamics of heavy quarkonium production at the LHC, an important step towards a satisfactory understanding of hadron formation within the standard model of particle physics.