The Mi-Ki breed has two possible coat varieties: smooth (close-lying, medium-length, no facial hair) and long (silky and longer, with moderate facial furnishings). Both coat varieties require some care, though the long-coated variety may need extra time devoted to styling its hair. See below for further details on Mi-Ki coat maintenance.
Both the smooth- and long-coat varieties need a moderate amount of care, so overall Mi-Ki grooming is not extremely time-consuming. Neither coat variety sheds much, but they may mat and tangle some (especially the long-coat ones). Mi-Kis with either coat variant will need brushing 2-3 times per week, but baths are only required occasionally (every 3-4 months should be fine). Depending on your preferred hairstyle, a Mi-Ki will need a haircut every 2-3 months; long-coated Mi-Kis may need occasional trimming of their facial hair to keep it clean.
Brush your Mi-Ki in the typical line-brushing fashion, using a slicker brush. (Those with long-coated Mi-Kis may also want to have a 2-in-1comb for working through mats/tangles.) If you do encounter a stubborn mat, first try to separate it with your fingers, then work through it the rest of the way with the comb.
Bathing: these little dogs are small enough to be bathed in the kitchen sink. Before the bath, give the Mi-Ki a thorough brushing; use canine shampoo (and conditioner, if desired), as human shampoo can irritate a Mi-Ki's skin. Wet the coat, then lather well starting on the back and working downward. (Don't forget the legs!) Rinse until the water coming off the coat is clear; towel- or blow-dry the coat, then give the dog another quick brush-through to make the coat look clean and neat.
Haircuts are recommended every 2-3 months. The Puppy Cut or Teddy Bear Cut are two popular styles for this breed; both can be done at home fairly easily, but it might be good to visit a professional groomer at least once, as the groomer can instruct you on how to do the cut yourself. Mi-Kis with long coats usually have medium-length facial hair, and that hair can get soiled with food when the dog eats, so owners often trim their long-coated Mi-Kis' facial hair every 4-6 weeks to help keep it clean.