The game will not prompt you or ask you for any referral code on its own. You have to go to the left of the main screen (colony, it is called) and enter the social panel. There you can find a button where you can enter a "mentor". There is where you should apply the referral code.
By doing so, you gain a 3 star card with high life points that will be very useful to begin the game.
The player who gave you the referral code will gain a random silver card when you enter it, the same card you get if you level up to level 10 and a gold random card if you get to level 50.
Hope that helps.
Fell free to use my own code, Zoargus , if you like (please )
Begginner tip: use your cards and gold to level up your hero and weapon first!