I communicate with our many cats all the time. I don't believe in training the cat as much as I believe in allowing the cat to train YOU.
Stop. Look. Listen. Our cats communicate to us all the time and I feel it is up to *us* to pay attention to what they are saying. We keep a multi-cat home and I can tell by the sound of a meow, which cat it is, where they are and most likely what they want. They are also able to communicate with me silently, simply by me observing them.
Malibu wants to jump onto the top of the rolltop desk, but doesn't jump, she just keeps shuffling her feet and looking at the top of the desk. I can tell she wants up there. So I ask her "Do you want me to lift you up there?" or I tell her "Hang on, I'll help you." and I can see her body language change. She stops shuffling, spreads her feet to stand more squarely and raises her tail as she looks at me. I stand up, scoop her up with my hands/arms and lift her to where she wanted to go.
I've never tried to give our cats choices about what food/treat they want but I feel we communicate all the time.