White Shepherds are direct descendants of standard German Shepherds, and thus have basically the same grooming needs. Sometimes called the White German Shepherd, grooming requirements for this breed are moderate. Though their coats don't tend to mat or tangle much, they shed a good bit year-round (and profusely during the twice-yearly shedding seasons), so they'll need brushing 4-5 times per week, if not daily. They only require baths every 3-4 months (or if they get particularly dirty or stinky), as bathing a dog of this breed too frequently will remove the water-repellent oils from its coat. And many owners give their White Shepherds shorter Puppy Cuts during the warmer months to help the dog stay cool.
The best brush to use on White Shepherds is a slicker brush; having a good shedding rake on hand is a good idea as well. Brush your WS frequently, using the slicker brush to go over the coat section by section in the direction of hair growth. Once or twice a week, use the rake in the same fashion. (During shedding season, you'll want to brush daily and rake 2-3 times per week.) If you're following the brushing with a bath: make sure to use an all-natural canine shampoo, as the human kind can irritate a dog's skin. Lather and rinse well, towel-dry, then give the coat another quick brush-through to make it look clean and neat.
For haircuts: WS owners often give their dogs Puppy Cuts, which sees the coats shaved to 1½-2 inches all over. The cut can easily be done at home, but it's a good idea to take your WS to a professional groomer at least once; the groomer can demonstrate how to do the cut yourself, and provide additional tips on grooming the dog in general.