The number one thing I can recommend is chewing VERY thoroughly, then waiting a minute or two between bites (especially after the first few).
Also, making sure food is sufficiently "wet" helps me quite a bit. I add salsa, greek yogurt (mixed with Ranch dressing mix), a spritz of low cal salad dressing, etc. to help meat and bulky veggies go down.
Once all your post-op swelling is over, this may not be much of an issue till you have proper restriction.
I personally have never gotten really "stuck." But I have eaten too much too fast and gotten sick from it. It's not the end of the world, but it's not pleasant. I usually do pretty well, but occasionally in an unusual situation, I'll have an issue. Learn from my fail: if you're at a restaurant and you're having a problem, excuse yourself to the restroom until it is resolved. : \