You can submit one Friend Code per account to receive 5 Diamonds. To do this, go to the Options menu and select Submit Referral.
If the Friend Code is valid, you'll receive your Diamonds immediately after selecting Submit. The player who referred you will get their Diamonds within 2-3 days. You can only claim rewards for the first five referrals submitted by other players.
My Singing Monsters on Steam is not cross-compatible with the mobile version. You can only refer players who are on the same platform as you.