Meaning of charges in a group? In my class, my professor said that since hydrogen is in group one, it has a charge of 1+. Does this refer to its ionic charge or to its oxidation state?
To go from being confused to less confused, here are some facts.


Hydrogen has one valence electron which can participate in reactions so it is a group 1 element.
Hydrogen is not a group 1 alkali metal, nor is it a group 1 compound, so simply stating hydrogen is in group 1  is ambiguous and confusing.  It is a group 1 element.  The word element needs to be included for the statement to make any sense.
Elemental hydrogen has no charge at standard conditions because it exists as dihydrogen gas, $\ce{H2}$.  If hydrogen gas were to be ionized it could hypothetically break into two ions, one with a +1 charge and one with a -1 charge.  If no ions are involved then the concept of ionic charge is irrelevant.
Elemental hydrogen, again as dihydrogen gas, $\ce{H2}$, has a zero oxidation state.  The oxidation state refers to a hypothetical charge of an element within a compound. If no compound is involved then oxidation states are irrelevant.  
Elemental hydrogen has an oxidation state of +1 in most compounds and -1 in metal hydrides because of an agreement within the International Union of Pure and Applied Chemistry (IUPAC). -- http://goldbook.iupac.org/O04365.html --  Oxidation states, as many of the concepts in basic chemistry, should be viewed as a tool to gain a rudimentary understanding of how compounds form.