Agreed on the reputable appearance and online presence. But also, make contacts and build a base of other reputable breeders. Be personable and ask lots of questions and find out about their collections and projects.

Don't... repeat... don't go to shows and be "that guy" who strolls around badmouthing other people, belittling animals at tables, lowballing people on their prices and then badmouthing them if they turn down the offers. Don't call yourself things like "best breeder around" or try to sound more knowledgable than you are. Don't ever say things like "I'll undercut any price!".

Being a good breeder is not just about having great animals, but also about being a part of the community. Even if it's just online, or even if it's just your local community... it's important.