If someone starts trouble on your talk page, don't respond in kind. Let it slide, or, if you have to respond, respond nicely. If it's really bad, contact an administrator--administrators are here to help. If it's an administrator, causing the problem or you don't feel comfortable talking to any of the admins, contact [[User:TTEchidna|TTEchidna]], the current Editor-in-Chief. If you don't feel comfortable talking to him for some reason, or need outside perspective, [[User:evkl|evkl]] or [[User:Archaic|Archaic]] are both available to field issues.
There are a handful of long-running feuds between some users. Kiss and make up. Bury the hatchet. Drain the bad blood. It would be a really great thing if every user who knew they had someone they really didn't get along with extended their hand--metaphorically--and apologized for wronging the other.
Accept that apology if it drops your way. Apologize back for anything you might have done to wrong them. Because we're all in this together, at the end of the day, and there's no reason to make enemies when you could have friends.