Tearstains are caused by a number of things - partially genetic [not much you can do about that part] but also environmental, and you can make simple changes that may effect the appearance of your pet.
#1 Keeping the face trimmed short around the eyes goes a long way in preventing eye irritations from hair that constantly gets into the dogs eyes.
#2 On a light colored dog wash the face once a day with a wet wash cloth - for some dogs it is as simple as that. Use plain water, no soap or shampoo, but you can also use witch hazel which is non irritating when it gets into the eye. Remove dust and grit from the eyes, wipe the nose and muzzle, massage the gums and rub over the teeth - this alone can make a considerable difference in the appearance of your dog.
#3. Use a paper towel or old washcloth - something that does no longer produce fibers and "woosles". Do not use cotton balls or pads, as they often leave tiny particles behind that irritate the eye and make the problem worse.
If you have a pup or dog that is prone to severe tear-staining, in addition to it having to do with how the face is build, you should also look at a number of other things to see if you can minimize eye irritation that causes excess tearing. Any single or combination of the below points can lead to tearstains, especially when your pup didn't have any when it first came to you, but developed them over the first week or two in your home. Sometimes it is simply that you do not know how to maintain your pup to its best appearance, and sometimes it is something in your home that causes this problem.
I think most often the #1+2 culprits are food and water., followed by mold in old carpeting, shampoos and other cleaning products that you use, in that order.
Dog food quality - there is so much junk in most commercial dog food today - from fillers to preservatives, food coloring and on and on - that upgrading to a better quality grainfree puppy food can often make the difference between tearstains or none, and also the overall coat quality. A lot of the nutrition poodles require, goes into making hair - crappy hair + coat usually comes from a combination of poor quality dog food, internal parasites and/or fleas, and poor hygiene/ bathing. We feed our puppies and dogs Taste of the Wild and they are doing nicely on this.
Dog Shampoo, perfumes + spritzes: pretty much any shampoo - even tear friendly or oatmeal - will generate some irritation when they get it in the eyes. If you ave a dog that is prone to tear stains, using a top quality natural shampoo is really, really recommended. It helps on so many levels, not only with the tear stains but improving overall coat appearance and skin, shedding, etc
My go-to recommendation is the Quadruped Pet Line - all of their products work well, but for a furkid with tear issues I would recommend the Yucca Tearless - it's great. Build your coat care routine around their product line and you will sidestep a lot of the trial and error care issues that new dog owners experience.
Refrain from using perfume or spritzes on your dog - it hurts their noses that work hundreds times better than ours. Give him/her a bath instead to freshen him/her up.
Household Cleaners used on flooring, carpet powders, detergent used for washing dog bedding.
Mold, dust, sand, pollen etc in carpeting [especially seriously old w-2-w carpeting]
Occasionally a dog has seasonal allergies if it gets relocated from one area in the country to another. I have seen this on occasions with spring puppies that move from the southeast where we are, to the northern or western states but this is usually a temporary issue until the dog gets used to the new plants etc in the area.
There are bunches of things out there, that [mostly don't] work - more or less. Wipes, pads, eye washes, bleaches, concealers, powders, etc etc. They all require religious application, washing, wiping [and often irritating the skin around the eyes, causing more tearing and consequently more staining. I've tried some of them over the years for those two of my white girls that tend to get tear stains, and thrown my hands in the air and resigned myself to having faces with rust colored streaks until I started to use the Nuvet Vitamins.
Angel Eyes is another product that often comes up in conversation and it actually works. BUT - - - it is a low grade antibiotic. So in order to reduce or avoid tearstains, you are basically having your dog on antibiotics for the rest of his/her life. Is it healthy in the long run? I think not. Long term use of antibiotics hamper the effectiveness when you actually need to use them [surgery, injuries, infection etc]. They also tend to mess up the stomach flora in the long run [permanently killing off beneficial bacteria in the gut, and therefor opening a new can of worms - literally in dogs]. And finally place a huge burden on the liver and other internal organs. Do you want to do this to your baby?
If you choose to go the supplement route, then go for a dog vitamin that is known to actually work on improving the immune system of your dog [and optimizes puppy growth and development plus helps with loads of other environmental health issues or prevents them as your dog ages] - and for me there is only one recommendation!
Nuvet Vitamins. Here is my page info about this.