How does the referral work? If you refer someone, do you get any prizes? Can anyone explain this to me? I'm really confused.

if a person is referred they need to do certain things/hit certain milestones for the referrer to get points. The Referred as to actually play the game, in other words

For referring someone, you get to put points into the following (assuming they play the game):
-Up to a 25% chance in getting a second scale from nurturing; this carries over to expedient nurtures, giving you the chance to get up to four scales per nurture, given the pet is being expediently nurtured
-Bred Egglings beginning at up to 10 points of incubation, meaning your egglings hatch faster, if you've bred them.
-I'm unsure on the final on this one, since I only have the other two unlocked 5/5, but you earn a percentage more gold from each battle you do.
You can see all this by going into the Settings section, under Account, and scrolling down.

Under the Account, you also have your referral code up, which you can alternatively use by copy pasting it, and giving it to the friend or person you want to sign up for the game.

Referring massive amounts of people, like Scath has said, is not the way to earn these points, though. You get points from the person you referred playing the game; doing battles, earning scales, and breeding pets.

*For the purposes of this, I can say that my words are based on the referral level of my account, which is 10. I have referred a total of 35 people, and I can firsthand say the finished benefits of 2/3 of the referral bonuses maxed to 5/5.