L.S.
At 16 months, I assume that your child is still pre-verbal or uses only a few select words. He probably does not have the language skills to use the phrase, "I'm done," or "I want to get down," so you're going to have to GIVE him these words. When he screams, you should say to him, "Are you all done? Do you want to get down?" and then try to teach him to say something like, "Get down." Then, when he says it, praise him!
Also, he is not too young to hear you use a phrase such as, "No screaming!" (Don't yell it, just say it very firmly.) While it IS okay to tell him to STOP doing a negative behavior, it's much more effective to SHOW and HELP him do a positive behavior.
I am unsure as to whether you are referring to him being in his booster seat at home or at a restaurant.
If you are at home, use your positive word phrase (Are you all done? Do you want to get down?) and/or your negative word phrase (No screaming) very firmly ONE TIME. If he does it again, the meal is over. Period. If he seems hungry 2 or 3 hours later (unless he did it at dinner time), you can give him a snack at this age. For children over 3, I would say to wait until the next meal to feed them.
If you are at a restaurant, of course this is much more difficult. For a child this age, distraction/redirection are probably the best ways to handle this (a quiet toy or a song, for example.) However, if that doesn't work, again, tell him "no screaming" in a firm tone, and if he does it one more time (and the key is ONE more time -- Don't repeat yourself over and over.) then you're going to have to remove him from the restaurant so he doesn't bother other diners. However (and this is important), make sure that you are not REWARDING his behavior when you remove him from the table. You should not allow him to walk around outside and explore or even be carried around in your arms. I would place him into his car seat, strap him in, and simply wait. If he continues to scream, just stand outside the car. If he is quiet, wait about 5 minutes or so and then you can try going back in.
The truth of the matter is that toddlers of this age really are not well suited for restaurant dining because they do have such short attention spans, but if you must take him out, you can try these techniques.