How would I heat treat a axe at home without knowing which metal it is made from

Contact the maker if known and maybe they know the steel, if not I'd heat it past non magnetic and quench it in oil, if it's not hard enough quench in water, then I'd temper it over the forge to dark straw/ nearly purplish color. I do the axes I make the same way.

~Jobtiel

Where at home might that be? The previous answer is how I would do it also. Test for hardness with a file.

Remember: if you are guessing at the heat treat you can't be upset if it selfdestructs during or afterwards.