You can add existing syndicated accounts to your Friends list in the normal manner (http://www.livejournal.com/support/faqbrowse.bml?faqid=61) or by visiting http://www.livejournal.com/syn/. This page lists the popular syndicated accounts on LiveJournal. If the feed you are interested in already exists as a syndicated account, but it is not in the list of popular feeds, you can use the form at the bottom of the page to add it to your friends list by entering the feed URL.
Only Paid and Permanent Account holders can create new syndicated accounts on LiveJournal. To do so, you will need to fill out the form at the bottom of http://www.livejournal.com/syn/ in the same manner as adding an existing account. You must enter the correct URL of the site's RSS or Atom feed. You cannot enter the URL of a regular HTML page on the site. You may be able to learn the URL of a site's RSS or Atom feed by contacting the webmaster or support service of the site.
If the feed URL you enter does not exist on LiveJournal, you will be prompted for a username. Please keep in mind that the username you choose must not be registered on LiveJournal yet.
Once you have entered your desired username, or if the feed URL already existed as a syndicated account, you will be taken to a page where you can add the syndicated account to your friends list, as well as your custom friends groups. See http://www.livejournal.com/support/faqbrowse.bml?faqid=61 for more information about managing your Friends list.
Once you have created a new feed, it may take up to several days for posts to begin appearing. If you have added it to your Friends list, there will typically be a large number of entries that appear at once on your Friends page. This is a one-time effect upon account creation.
General information about syndication on LiveJournal can be found at http://www.livejournal.com/support/faqbrowse.bml?faqid=178.
Edit: I updated the FAQ with a very slightly modified version of this. I didn't wait 48 hours since it was originally suggested a while back, and it really is a necessary change. Please comment or post a new entry if you notice any problems with it, though (as you should do with all FAQs!).