Adsorption of hydrogen atoms on a single graphite sheet (graphene) has been investigated by first-principles electronic structure means, employing plane-wave based periodic density functional theory. A 5 x 5 surface unit cell has been adopted to study single and multiple adsorptions of H atoms. Binding and barrier energies for sequential sticking have been computed for a number of configurations involving adsorption on top of carbon atoms. We find that binding energies per atom range from approximately 0.8 to approximately 1.9 eV, with barriers to sticking in the range 0.0-0.15 eV. In addition, depending on the number and location of adsorbed hydrogen atoms, we find that magnetic structures may form in which spin density localizes on a square root(3) x square root(3)R30 degrees sublattice and that binding (barrier) energies for sequential adsorption increase (decrease) linearly with the site-integrated magnetization. These results can be rationalized with the help of the valence-bond resonance theory of planar pi conjugated systems and suggest that preferential sticking due to barrierless adsorption is limited to formation of hydrogen pairs.