Tear staining is a big problem in Maltese dogs.You should always take your dog to the veterinarian to make sure there are no medical problems such as blocked tear ducts, allergies, infections or other issues that need to be addressed by a veterinarian. If you are breeding your Maltese, make sure that genetics do not play a role in tear staining as well.
Create a routine. All dogs learn best with consistency and it's much easier to clean the area when it is not so stained. Miss a couple days and the substance returns and is difficult to remove again. The best time to start is right after your dog has been professionally groomed. The hair around the eyes is short and clean. Maintain that grooming as much as possible.
Pick a spot for your daily grooming and have everything you need close by in one place. You'll need a towel or pad for your dog to sit on and a plastic container with the daily grooming supplies, treats and medicine. Having everything in one spot makes it easy to grab and take along when you travel.
Soak a cotton ball with plain saline solution (found in the drug store contact lens section). It's inexpensive. Start at the inner part of the eye closest to the nose and wipe out towards the ear. Get a new wet cotton ball and wipe the other eye. Give a small treat after each eye is cleaned.
Wipe the mustache hair under the eyes with a new wet cotton ball or wash cloth, wiping down, away from the eyes. You are removing any eye debris and food that collected between the eyes and mouth. There are solutions for whitening the hair in this area. Be careful not to get solution in the eyes. Give a small treat.
Wet the comb (with tap water or saline) and gently comb the mustache area to smooth it down. This is a sensitive spot, so be gentle and don't pull at the knots. Trim the knots out with baby nail scissors (rounded ends) so you don't accidentally injure your dog if he jerks away or tries to bite. Reassure your dog and tell him how well he's doing.