Yes, you pay ether for them. You can either buy two to start breeding, or you can buy one and then pay less than it would cost to buy a cat to have someone else's cat breed with yours and you get the baby. Parents cannot breed with babies. Then, you can either sell it or keep it to breed with another one. Different generations have different ether values, as do cats with rarer qualities. The generations start at zero '0'. Two zero cats would have a gen 1 baby. Two gen 1's would have a gen 2, and so on. You can breed between generations, but it lowers the value of your kitten, because it will be a lower gen cat.