Read the book T.S. Eliot's "Old Possum's Book of Practical Cats." It's short and makes the whole show understandable. Without it, you'll be lost. Having read it, all of the strange names and references suddenly will make sense.
Be prepared for the structure of the show. It's not intended to be a linear narrative. Instead it's more of an abstract series of vignettes all about a tribe of cats reuniting for one night a year to celebrate and decide which one of them will journey to the Heaviside Layer to be "reborn."
Listen to the music, and get familiar with the tunes. The lyrics are pretty much all in the Eliot book. The musical styles vary so much from song to song that it can be jarring at first.
See the film version. Its pace seems slow to the uninitiated, but with the preparation mentioned earlier, the film will feel quite different to the trained eye. There are thought-provoking themes of aging and death and community interwoven with more whimsical numbers that give the work sparks.
Go see the show live. There is nothing like the experience of watching professional actors and actresses interpret such great material in a beautiful theater.