Summarize:

Diaphragm calls, or mouth calls, are tricky to use, but their range makes them popular with turkey hunters anyway. Unlike box and slate calls, they aren’t held in your hands. Instead, a mouth call is a rubber or latex organ that fits in the mouth, up against the palate.  Single-reed calls have the best range: you can make a wide variety of noises, and make those noises carry farther, with them. However, they’re hard to learn.  Double-reed calls are a bit more limited, but they’re much easier to use. Since mouth calls don’t require the use of your hands, they’re convenient, but require learning a different set of motions. Find a quiet place where you won’t be interrupted, and get your mouth used to the way it feels to have the call inside it. Here are some exercises you should try.  Start by placing the call in your mouth. Keep the open end facing outside, then push the call up to the roof of your mouth with your tongue. Exhale so that the air is forced between your tongue and the call. Press your tongue hard against the reed, then blow. You will produce a higher sound this way. Now press more gently. With low pressure, the sounds will be lower tones. Exhale syllables, such as "chuck" or “pip,” between tongue and reed. This will help you hear the distinct sounds they produce. Now that you’ve gotten the idea of how it feels to manipulate the call, you’ll want to ensure a custom fit. If it feels a little too large in your mouth, carefully trim along the edge with clean scissors, then pop it back in to check the fit. Remember to trim conservatively--you can always cut more if you need to. The classic yelp isn’t hard to do with a mouth call. Try saying the word “chuck” repeatedly. Experiment with different volumes and pitches to mix it up, and remember: a yelp is the first call you’ll learn on the mouth call, but not the only one. Toms are usually the ones who cackle (or gobble), while hens are the chief cutters. There may be a sex difference in the way these sounds are deployed, but the motion for each is the same. Simply place your call in your mouth, and say “kit kit kit” several times.  Make the sound quicker for cackling. Try listening to recorded cackles and gobbles until you feel you can get it right. Slow the sound down a bit to cut. Purring is especially tricky on the mouth call. Some mouth call users prefer fluttering their lips around the call (as if they're blowing a raspberry), while others roll a syllable in the back of their throat (as if they're gargling). Experiment to figure out which works best for you.
Buy a single or double-reed diaphragm call. Practice moving your mouth. Trim the call to fit your mouth. Begin yelping. Cackle and cutt. Practice purrs.