Long Game promo codes can be redeemed by tapping the friend icon at the bottom right of the home screen then tapping the gift top at the top left. On the next screen tap the words "Redeem a Promo Code" then enter your code.
You can invite as many people as you wish, and for each that joins you will receive 1000 Coins. However, you can only be referred by one person. This means that you can only put in one other person's promo code.
Long Game sends out new codes in emails, newsletters, and special promotions from time to time.