How does the location of hydrogen on the periodic table differ from the locations of other nonmetals?

It's special, because it has only one electron, while the ideal "noble gas" configuration (helium) would call for two.

EXPLANATION:

So in one way it could 'try' to gain an electron as any element from halogen group (F-Cl-Br...) would do.
On the other hand it could lose its one electron, in which case it would belong to the alkali metals (Li-Na-K...).

In practice, H mostly shares its electron, either by covalent bonds, or by donating an electron and working together with H2O to form the H3O+or 'acid' ion.

In short, H is too special to to put it in a specific Group.