This is a (rather rough) draft only. Commennts or corrections more than welcome. Expansion also welcome; it's kind of short.
ETA: Edited to incorporate suggestions (as of feb 4). Was going to add information about ?mode=live, but that doesn't seem to be working for me. *eyes it suspiciously* maybe because I'm using a custom s2 style, dunno.
"How do I know when my friends have posted new entries?" (Probably under "Friends")
Your Friends page (http://www.livejournal.com/users/exampleusername/friends) will display entries from users on your friends list, and will update with any new entries when you load the page. (If you are not seeing updates that you know exist, please see http://www.livejournal.com/support/faqbrowse.bml?faqid=92 for possible reasons and for troubleshooting suggestions.) However, LiveJournal does not explicitly notify you of changes to your friends page.
Some downloadable clients have the ability to notify you when there are updates to your friends page, often by flashing the system tray icon or generating an alert. (This notification will only work when you are logged into the client, and when you have an active network connection.) However, this feature will only work for users with Paid or Permanent accounts.
You can also use the RSS feeds that LiveJournal provides (http://www.livejournal.com/users/exampleusername/data/rss/) to generate notifications of new updates for one or more users on your friends list, using an RSS reader. LiveJournal cannot recommend any specific RSS reader to use, or provide assistance with using such a program.
* managing friends list?
* RSS info
* Downloadable clients
* client flashing?