When cleaning acrylic furniture avoid: windex, or ammonia based cleaners, they, over the long term attack the finish.
Also, just clean when dusty or fingerprinted, not as a routine. Use a soft, clean, terry cloth towel, maybe dampened.
There are quite a few commercial cleaners available, some aerosol, but I find them unecessary. Sometimes, a haze remover,
Novus is good.
It is like toothpaste, or like buffing your car, with circular motion. I don't sell it, but it is readily available in small bottles, get the #3 for best results.
I see lots of acrylic tables acually manufactured Mid Century, some in pretty good shape. But direct sunlight will over the years discolor the material.