Silky Terriers' fine, smooth, long-haired coats are comparable to human hair, so they will need frequent coat care. Silky Terrier grooming should happen 4-5 times per week (if not daily); they will need baths every 3-4 weeks, and--depending on the grooming style--an occasional trim to keep the coat manageable.
To brush: first wet the coat with mist from a spray bottle; many Silky owners add a leave-in conditioner to the water to keep the hair, well, silky. Use a slicker brush to comb through the hair, starting at the head; slowly work through the body hair and finish at the tail. Use a greyhound comb to gently work through stubborn tangles. If bathing the dog, finish the brushing process first, then bathe the dog in lukewarm water, using gentle canine shampoo and conditioner (available at pet stores). Then towel- or blow-dry the coat, and finish with another quick brushing.
To give the dog a trim, use scissors or clippers. Silky haircuts can be tricky, so it might be a good idea to learn from a professional groomer, who can advise you on how to groom a Silky Terrier; video on YouTube or comparable sites offer further instructions.