When a man and a woman, or a man and a man, or even a woman and another woman, love each other very much, they go ask god, and god says, yes or no, if he says yes, they are married, if he says no, they get sent to hell through a trap door like thing that god triggers by pushing a button behind his desk. Hope this answers your question.
Propose, go to your local priest/religion head, say your wedding vows, exchange rings, sign your marriage certificate, party, first night together, and there you go...you're happily married. Of cause when you are a pet, you don't need to go through all the above trouble, just jump to the last above mentioned portion. Done.