A single hydrogen atom can form one covalent bond. A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms, according to Georgia State University's HyperPhysics site. The atoms share valence electrons, which are in the atom's outermost shell. Hydrogen has one electron to share.
Atoms desire a full valance shell, which gives them a stable balance. The sharing of electrons allows atoms to attain this stable electron configuration. Hydrogen has a 1s valence subshell, which can hold a maximum of two electrons. Hydrogen covalently shares this single electron with other atoms needing extra electrons to fill their valence shell. For example, a fluorine atom has a valence shell containing seven electrons, yet it has a maximum capacity for eight electrons. Hydrogen shares its one electron with fluorine, and fluorine shares one of its valence electrons with hydrogen, giving both atoms a stable electron configuration.