Harassment generally happens in two forms: harassing comments by another user posted in your own journal, and harassing posts about you in another user's journal. There are different steps you should take for each type of harassment.
In either case, in order for the Abuse Team to consider taking action, the harassment needs to be one-sided. The Abuse Team will not mediate "flame wars" between two parties, and will not take action in cases where both users seem to be equally at fault.
HARASSING COMMENTS
If someone is making unwanted or harassing comments in your own journal, the first thing that you should do is ban them from commenting in your journal. If these comments happening in a community, you'll need to contact the community maintainer to ban the user from commenting.
If the user then begins posting anonymously, you can either ban anonymous commenting from your journal, or set your journal so that anonymous users can only post "screened" comments, which means that you'll have to approve those comments first. You should also enable Comment IP Logging for your journal.
You can also make sensitive entries Friends-Only, which will block everyone from viewing them except the people on your Friends list. See
http://www.livejournal.com/support/faqbrowse.bml?faqcat=security for more information on the various security features.
Because there are tools to block users from commenting in your journal, the Abuse Team generally won't take action in cases such as these. If you do feel the need to report them, however, be sure that you include links to all of the comments in question, and do not delete the comments until after the Abuse Team has reviewed your case.
HARASSING JOURNAL ENTRIES
If a user is posting journal entries that make reference to you in a negative fashion, first ask yourself whether a casual viewer of that journal would have enough information available to identify you. In order to be considered abuse, content must identify you in such a way that a random reader could identify a specific person in the physical world.
Generally, this means that the poster must include your full name, your address, your telephone number, or other uniquely identifying material or information. First names, Internet nicknames, LiveJournal usernames, and other forms of non-identifying information do not count as violations of the Terms of Service.
If the material in question does contain a way of uniquely identifying you, you can file a report with the Abuse Team. Be sure to include links to all pertinent entries in the user's journal. The Abuse Team will not investigate these cases unless reports contain specific links to investigate.
FURTHER READING
How do I contact the Abuse team?
http://www.livejournal.com/support/faqbrowse.bml?faqid=105
How do I ban/unban a user from commenting in my journal?
http://www.livejournal.com/support/faqbrowse.bml?faqid=20
How do I control who can post comments in my journal?
http://www.livejournal.com/support/faqbrowse.bml?faqid=23
What is comment screening? How do I set my screening options?
http://www.livejournal.com/support/faqbrowse.bml?faqid=134
What is Comment IP Logging? What do you mean, "this user is logging my IP address"?
http://www.livejournal.com/support/faqbrowse.bml?faqid=66.
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