Referrals go through several stages before you actually get paid. You can track them through your referrals page. (Click 'Referrals' from the menu on the left, after logging in.)
At first, when you've just sent out a link, nothing happens. Once the recipient takes some action (whether creating an account in the case of 3% introductions, or contacting the tutor in case of 6% recommendations) then the referral will appear on your referrals page (with £0.00 due to you) to show it's being tracked. (Unless it's a self-referral: these are tracked slightly differently, so the 6% part of it won't show up until the client has booked a lesson with you.)
Referrals become eligible for payout once the tutor giving the lesson has been paid for it, which is 1-2 weeks after the lesson happens, on a Friday afternoon. Once that happens, the amount you're due will show on your referrals page and it will become eligible for payout. Then the payment takes place once a month, and includes all eligible referrals up until the end of the previous month.