At http://www.livejournal.com/create.bml page, I think there should be another box, something like, "Who told you about Livejournal?" with a box, where a user can type in a username, i.e. TSUTTON
Then the referral gets counted in my profile page, /userinfo.bml?user=tsutton with this line:
No. of referrals: xx
where xx is the number of users I've referred to Livejournal.