If you see tear drops or dripping eyes, simply wipe them away with a damp cloth and tap water. When caught early enough, small tear stains can be treated easily.  Get a cloth damp and then gently wipe the fur around your pet's eyes. There is no need to add soap, especially if the tear drops are very fresh. Be very gentle, however, when cleaning around your pet's eyes. You do not want to get water or the edges of the cloth in their eyes, as this can cause irritation. Tear stain removers can be used to address set-in tear stains. While these are not necessarily a medical concern, they can be unsightly. In some cases, crusty stains can cause eye irritation for dogs and cats. You should always talk to your vet about a safe tear stain remover for your pet before purchasing a product at a pet store or online.  Herbal or natural products may be safer on your cat or dog than harsher commercial products. However, labels can sometimes be misleading and a "natural" product may contain a lot of synthetic chemicals. This is why consulting a vet is important. You likely will not need a prescription for a tear stain remover. However, your vet should be able to give you a recommendation for a commercial product to purchase. Your vet's office may even have the product in stock for you. Over-the-counter products are not safe on all dogs. Small dogs especially may be adversely affected by over-the-counter products sold to eliminate tear stains. Go over instructions for use carefully with your vet, especially if your pet has an underlying health issue that could affect how the product is applied. Make sure to read reviews of any products you look at that promise to remove tear stains. You can read reviews online. You can also type the names of various products into a search engine. Some products are not FDA approved and have a bad reputation for causing eye irritation and other health problems in cats and dogs. For safest results, only browse and compare products recommended by your vet. In dogs, tear stains can sometimes be caused by the excessive production of molecules called porphyrins. This may be correctable via antibiotics. If your dog is prone to excessive tear stains, talk to your vet about whether antibiotics could help. Do not choose a product without veterinary supervision.  Many antibiotics are only available as prescriptions from your veterinarian. Your vet cannot legally prescribe an antibiotic without first examining your pet. Keep in mind antibiotics have not been strongly linked to reducing tear stains in dogs, but some people have had success with products known as doxycycline, metronidazole and enrofloxacin. If your vet suggests one of these products, use it only as your vet instructs. With luck, it will clear up tear stains on your dog. However, you may have to resort to other methods if antibiotics are not successful. If the stains are very bad and crusty, you can see if you can have them removed at the vet's office. Your vet may have technical staff on their team who are able to remove tear stains. You can also take your dog or cat to a groomer to ask about removing tear stains.  In addition to removing already existing stains, ask the groomer or vet tech to trim the hair around your pet’s eyes where tear stains and eye crusts tend to accumulate.

Summary:
Wipe your animal's face with a damp cloth. Consult your vet regarding a tear stain remover. Compare recommended stain removers. Talk to your vet about antibiotics. Ask a groomer or vet to remove the stains.