For some really good examples of cat photography, have a look at the work of the photographer Tony Mendoza. He published a book recently entitled Ernie: A Photographer's Memoir, which is still in print and available from the usual retail outlets. Unfortunately, his earlier book on the same subject seems to be out of print.
Though Ernie does not contain specific advice on how to photograph a cat (in this case Ernie, though I assume the procedure would generalize to other cats), Mendoza describes the overall process as follows:
I photographed him every day for two years and made around 10,000 negatives.
That process seems to work very well for many
photographers.
Garry Winogrand is perhaps the most well-known proponent of this
technique.