First, grow an alligator hide.
We’ve looked before at public shaming on the Internet: "Good? Bad? Think before we retweet? "One key irony is captured by commentator Ed Driscoll in the title of a recent post, “How an Internet Stuffed to the Gills with ‘Nonjudgmental’ Users Became a Shame-Storm.”
Indeed, many of the worst offenders at starting unjustifiable persecutions probably think of themselves as non-judgmental. And there are a lot of them out there, launching persecutions on a a hair trigger in many cases.
Driscoll worries that shaming harms society because it causes people to hide bad beliefs:

And you haven’t even necessarily changed what they say in a good direction, because people who are afraid of unjust attacks aren’t afraid of being punished for saying things they know they ought to be ashamed of, but of being punished for saying something they didn’t know would attract this kind of ire.

Unfortunately, his argument assumes good will on the part of the shamer. I believe otherwise: Such people typically celebrate their power to destroy those with whom they disagree. He notes, more persuasively, that “An even greater cost is that shame itself starts to lose its power. When outrage of the week becomes outrage of the hour, the audience starts to check out.”
Which, as it happens, leaves adult toddlers, possibly emotionally damaged themselves, in charge of the frenzy they whipped up against some person otherwise unknown to them. The boundless freedom and voluntarism of the Internet is its greatest weakness, as well as its greatest strength.
What if it suddenly happens to you?: You said something to which you attached little importance, and abuse and filth pour into your box (and your employer’s?).
It once happened to me. Internet atheists did not appreciate something I said in defense of the Catholic Church. So for a while, I spent a lot of time deleting dozens of messages at a time, unread. In between going for walks in the cold, clean air. I wondered what these people did for a living. Where did they find the time?
Since no can “fire” a self-employed person like me, it all just died down after a while. Others have not been so lucky. Mark Fitch offers some useful advice for intended victims at the Federalist: in “We Are Legion: Don’t Let Internet Culture Amplify Idiots.” Recall, he says, that “Two thousand people is a drop in the bucket of the overall population, but when they all turn and look at you it can feel overwhelming.” Yet

It was recently revealed that nearly 70 percent of the criticism lobbed at Rush Limbaugh (which is ample) comes from a small group of activists that have devoted their lives to attempting to make his miserable. However, to view coverage of Limbaugh in television and Internet media, you would think that the entire country is listening and vastly offended at everything he says.

I am glad that the Hush Rush movement has so far flopped. No one is forced to listen to him; I do not, as it happens. But storm shamers, like other storm troopers, tend to be small, elite, purpose-driven groups—whose success lies in making both their victims and onlookers believe they are invincible, so resistance is futile.
He also notes that the Internet offers these career- and life-wreckers a great advantage over boots-on-the-ground conflict. One person can use a number of different Internet personas “that can spew any amount of nonsense and vitriol with no accountability or personal reflection whatsoever.” Earlier, we saw how click farms can boost one’s apparent popularity, as low-paid workers in developing countries post fake likes and follower accounts and profiles to customers’ sites. Thus it should not surprise us that the angry sea of hostility may be a fake too. Maybe all that hostile mail I received was coming from two people on unemployment insurance in a trailer in Boise, Idaho… 
But keep in mind that moral perceptions have changed too. As Dave Pell writes at Medium, “I’m still old enough to remember when the people who recorded and leaked private phone calls were considered the villains?” Not now.
In the eyes of many, hacking information from private e-mail accounts and leaking it to the storm shamers is virtuous if it allows the current pariah to be shamed. So, as he puts it, only if your communications are “the verbal equivalent of wind chimes” do you have nothing to worry about.
Personally, I chose, as noted above, to just ride out the storm. Eight years later, I was none the worse for it. But then, I wasn’t running for office either, and had no unscrupulous face-to-face opponents to deal with. If just riding out the storm is not an option, Wall Street Journal drama critic Terry Teachout’s advice re social media should be heeded:

Use them prudently and they can be a source of enormous pleasure and profit, but never forget that the sharks of cyberspace lie in wait to bite your hand off. They don’t care about you. In fact, you don’t even exist to them, save as an abstract symbol of their preferred causes. What they want, ever and always, is power, and they’ll happily eat you in order to get more of it. If you’re not prepared to bite back—hard—then stay out of the deep end.

Considering that Twitter only got started in 2006, many of us have not really had time to absorb the impact of these changes.
A harrowing account from a victim, Jon Ronson, who wrote a book, So You've Been Publicly Shamed, detailing his and others’ experiences:
 

Denyse O’Leary is a Canadian journalist, author, and blogger.