A white leather court shoe looks best on day one and on day four hundred. The bit in between is where people give up.
Wipe them after each wear with a dry cloth: most marks are dust that has not yet been walked in. Once a month, warm water, a soft brush and a pH-neutral cleaner, then let them dry away from a radiator.
Do not put them in a machine. The drum breaks down the glue on the sole, and a pair that would have lasted two years starts gaping at the toe in six months.