Id probably do a bunch of easy tests . Like specific gravity, color and crystallography under polarized light microscope.
The opacity on thin slices is a good diagnosis(unless it IS a glass cullet left over from something like stained glass manufacture).
Age dating is easily done by a geology student proficient in polarized light mmicroscopy.
There aresome fancier tests (which usually arent done because of cost). Secondary Ion Mass Spec would identify the metal components (Green obsidian is usually the result of air , not metals. Colored glasses are made of iron or chrome inclusion.
Id but it up and put it in a tumbler to see the layering close up. I would NOT put it in a mineral saw (diamond blade) because Ive had students really screw up an expensive blade by exerting too much force on the "infeed" and then the saw blade starts plucking diamonds and the whole thing starts smoking and the saw blade will be ruined.
Usually the best way is to just keep in mind where he found it and what was the makeup of rocks there. (Was there an obsidian deposit?) or was this just found in a pile of other rocks and clinkers?
Since obsidian degrades into perlite by taking on water, we dont find any obsidian in really ancient rocks,(Usually no older than K)