These dogs have medium- to long-haired, silky, double-layered coats that shed a good bit, but typically stay clean and don't require trimming--so Borzoi grooming is not very time-consuming overall. Borzois shed regularly for most of the year (and profusely during the twice-yearly shedding seasons), so they'll need brushing about twice a week to keep the shedding under control. The silky coats are naturally dirt-resistant, so baths are only required when necessary. Haircuts aren't needed at all.
Brushing a Borzoi with a pin brush is best--and in fact, groomers say using a wire slicker brush on these dogs can permanently damage their coats. A good 2-in-1 comb might come in handy as well. Brushing should happen twice per week, and daily during shedding season. To brush your Borzoi: first wet the coat with mist from a spray bottle (and you can mix in a little conditioner or de-tangler, if desired), then brush the coat section by section, moving in the direction of hair growth. You can use the 2-in-1 comb on the neck ruff, rear end, and tail if needed. If you encounter a tangle or mat, first try working it out with your fingers, then finish working through it with the comb or brush.
Borzois normally stay pretty clean, but if the dog is especially dirty or stinky and needs a bath, be sure to give it a thorough brushing first. Also be sure to use canine shampoo and conditioner, as the kind made for humans can irritate a dog's skin. Lather well, rinse completely, towel-dry, then give the coat another quick brush-through to make it look silky and clean.
Most Borzoi owners say they prefer their dogs' coats at their natural, full length, but the coat can be clipped to make it more maintenance-free. You can learn to clip the coat yourself, but it's recommended that you take your Borzoi to a professional groomer at least once. The groomer can demonstrate the proper haircut method and provide grooming tips in general.