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First, you visit the vet - to determine if the tearing is due to extra eyelashes - turning inwards & scratching the eye causing irritation and tearing (etc). Often, if this is the case the eyelashes need to be removed. If you do not get rid of the eyelashes - the tearing will continue and look UNSIGHTLY and cost you more (in the long run) esp if the dog gets an eye INFECTION of ULCER. Yes, at this point, your dog (may or may not) have developed an eye ULCER from the irritation - so again, this may need to be treated, to heal.
Your groomer may also need to trim the fur/coat around the eyes. There are coat cleaner (wipes) for tears stains (that work to some degree) and ADDITIVES - such as "Angel Eyes" you put in the dog's food to lessen or stop the tearing AND the common ensuing yeast issue (from all the moisture).that allows the discoloring to happen. Again, your groomer or vet can make suggestions of products & actions - to help you with this staining.
Anonymous
There are 2 recommended daily wipes and 2 recommended removers:
http://www.allpoodleinfo.com/poodle-tear-stains
Earthbath All Natural Specialty Eye Wipes for daily cleaning.
Petpost Tear Stain Remover Wipes ; these are pre-soaked daily wipes for stubborn stains. ...
SPA by TropiClean Tear Stain Remover ; for a liquid remover that is surprisingly effective.