Giving a cat free food? That's the easy part. A mere 60 grams of meat feed should do the trick (to tame; daily amounts are shown in the infobox). And, of course, once you feed a cat, chances are it'll come back for more the next day. And the next. And the next. After one day, they might even give you the privilege of letting you pet and take care of them (a 75% chance, it turns out). However, they will always insist that it is they who have tamed you.