Hello and welcome! Can I first direct you to the LFR group
which is the hub for all LFR-related info and has a separate set of forums. Posting here's fine, but people are beginning to move over to those forums and the blog and wiki there contain various bits of very useful info. I've not yet had time to make a 'getting started' entry in the wiki, but it's something I do keep meaning to do!
To get WotC to enable your D&D Private Play co-ordinator status, follow the instructions in this WotC Customer Service article: wizards.custhelp.com/cgi-bin/wizards.cfg...
For now, you'll need your own RPGA/DCI number and you'll also need to visit a store which runs D&D or Magic events and ask them for some membership cards for your players. The plan in the near future is to remove the need to track and report private play of LFR - and make the adventures far more easily available - but that's waiting on some technological steps. For now you should order and report adventures played using the online system.
Note that an official Living Forgotten Realms session/table has one GM and between 4 and 6 players (not 3 or fewer or 7 or more). Both the need to report and the table-size limits are difficult for anyone to enforce, but they are the rules at the moment. I do not expect the table-size limits to change as WotC has done a lot of thinking about D&D and consistently believes that the further you go away from five players, the worse the game is for everyone.
I hope that helps! Feel free to ask any questions here or in the LFR group.