I've not have to clean an actual "stain," but did have clear crud from below the inside corner of her eyes from time to time.
To clear the crud, I just used plain water on a cloth, and then a narrow tooth comb.
My niece has a different breed light coat pup that develops tear stains. As I understand, this is sometimes symptomatic of a health issue.
Here's an AKC article that may be helpful.
AKC Staff, "
How to Prevent Tear Stains on Your Dog's Face," 7 July 2015,
AKC.org.