You need a cat that is 4-star in relationship, you also need a bouquet to get a mate with (4-star relationship cat needed), you can buy it in Java's Cafe, once you already have mated. You can click on your mate to interact everyday, if your mate have 4 hearts in relationship menu, you need to buy a heart-shaped diamond from Java's Cafe, to marry your mate. Also, you will have kits by clicking your mate in your den or outside, BOOM! Here you go!
I hope, this helps!