Back during the good ole days of the Internet Websites didn't care much about their Users Security, in fact the Virtual Environment was quite relaxed in regards to End User Safety. This wouldn't last for long, and with the Introduction of Web 2.0, and many Tragic Circumstances over the years most Websites began to allow Full Anonymity to their Visitors.
Anonymity is great, however a lot of people use the Anonymity Cloak as a means to behave badly while Online. Cyber Bullying much like Offline Bullying is a Huge problem Online and it knows no Boundaries.
It's true that modern day Blogs, Communities, and Websites offer it's Users Tools to combat such Activity in the form of a "Flag This" or "Report This" Button.
Although a big step in the right Direction, doesn't always solve the problem. These individuals can simply create another Account under a false Name and continue to berate or Stalk their Victims.
Some Social Networks like Facebook for example use a Network Banning Protocol to restrict the most Venomous Users, again this is only a Temporary Fix especially if the Individual knows how to Ban Evade.
The best way to Solve the issue is to Contact the Source.
You will need a Website, any will do even a Free one such as Blogspot.com. Set it up, doesn't have to be fancy just a single page with no Content. If you prefer you can Populate it with any words of wisdom you want.
Find a Visitor Counter Service Online. Visitor Counters allow you to see the total number of Visitors to your Website and what all Pages they clicked on. You also get the IP of each and every Visitor. I'd go with http://www.statcounter.com
Embed the Visitor Tracking Code into you're Web page(s) and test it out by clicking on that particular page. Within a few moments if not Immediately, you will see you're Internet Address and depending on the Service you went with, additional Information about the Users Browser and Operating System.
This will all be found within your Visitor Counter Account, make Note of your IP Address. In fact, with StatCounter you can even Label your own IP Address so you can distinguish your Views from that of your Target.
Navigate you're Mouse to the Browser's URL Box where your Page resides. Right Click, Select All. Right Click Copy. You may want to use a URL Shortening Service such as Bitly.com Shorten it to something that will get your Target's attention. Example "Police beat up Pot head for loose change" (If your Target is a Doper).
In order to Ensure that you get your Targets Information Only, Private Message them with the Link pasted if possible. If you're using Twitter, just DM them, or what have you. You want ONLY them to click the Link.
Once you have their IP Information, you will both be on equal Playing Fields and it's as simple as reporting them to their ISP's Abuse Department through an E-Mail. This should solve the Problem, although if it doesn't there are other remedies to seek which aren't so Legal or Ethical.
Contacting The Abuse Department:
Once you have the Target's IP and Internet Service Info (StatCounter Etc) then proceed as follows.
Simply take Note of the Internet Provider (IE. Comcast)
Next go to Google, type in "Comcast Abuse Contact" in this case it's "abuse[AT]comcast.net" replace "[AT]" with "@". Be sure to include your Complaints and all detailed Logs if Available of the Abuse. Time stamping is a Plus. Also don't forget to include the Abusers IP Address.
Depending on how fast you Type and your Internet Connection you can have this all setup and done within 7 Minutes. There are many ways to Obtain this Information, but due to Patches TOS this one is a stripped version for Legality Purposes.