Should have had instructions. Did you get the mandrel and expanding bushings?
Enneyhow, short tut.: turn the larger/longer portion (body or barrel) using a 3/4" bore and the larger bushings. Make it about 4" long.
Turn the smaller/shorter portion (stopper) using a 1/2" bore and the small bushings, it should be 1 1/2" to 2" long. Turn your tennon so it will fit snugly into the barrel. This can be tricky. You want it tight but not so tight you risk cracking the barrel. For your first, final fitting will probably be with sandpaper.
Put the reed and plug into the stopper facing into the barrel. (towards the user) [BTW, I'm assuming this is the type of call that is assembled that way, 90% of them are. a very few are reversed)
Tomorrow, if you are still not understanding, I'll take a couple pictures and post. You said "game call" what kind is it?