Hydrogen is classified as a non-metal based on its physical properties. Metals, located to the left of the stairstep elements, have the properties of being shiny, conductive, malleable (can be made into sheets) and ductile (can be made into wire). Since hydrogen has none of these properties it is obviously not a metal.
It is located at the top of group one of the periodic table because the periodic table is arranged so that all elements in a given group have the same number of outer or valence electrons. All elements in group one have one valence electrons, as does hydrogen.
In terms of its chemical reactions hydrogen can form both covalent and ionic bonds. It bonds covalently with other non-metals such as nitrogen, sulfur, oxygen, carbon, etc. In fact, there are more chemical compounds which contain hydrogen and carbon (hydrocarbons) than all other chemical compounds combined.
It forms ionic bonds in acid solutions such as hydrochloric acid, nitric acid, sulfuric acid, etc. in which it exists as a positive ion and determines the pH of those solutions.
Hydrogen is also unique in that it can form chemical compounds in which it has an ionic charge of -1. Examples are the metal hydrides such as LiH, NaH, etc.
Hydrogen has three primary isotopes, H-1 (protium), H-2 (deuterium), and H-3 (tritium), with H-1 being the most common and abundant element in the universe.
H-2 is used in nuclear applications (see link) and H-3 is a radioactive isotope that once was painted on the hands watches so they would glow in the dark and be visible at night.