Instructions:

1. Find Gertrude and ask her about her problem. She'll tell you to go talk to her boys Wilough and Shilop in Varrock square.
   
   
   
   
2. Go South behind Gertrude's house and pick up the Doogle leaves. Use them on your Raw sardine to make a Doogle sardine.
   
   
3. Talk to Wilough and Shilop, and they'll tell you where they last saw the cat, except you have to pay them 100 Coins.
   
   
   
   
4. Head West to the house directly South of the building with the anvils (just South of the West bank), climb up the ladder and try to to pick up Gertrude's cat Fluffs. It will hiss at you, and a message will appear saying it might be thirsty. Use Bucket of milk on it and try to pick it up again, only to find out it's hungry this time. Feed the Doogle sardine to the cat. Try to pick it up one more time and find out it doesn't want to leave and can hear kittens mewing in the distance.
   
   
5. Head over to the building directly to the East, search the jiggling crates for Fluffs' lost kittens. Once you have found the Three little kittens use them with Fluffs and you will see a short cutscene. They will then run back home to Gertrude.
   
   
6. Walk back to Gertrude's house. Gertrude will thank you for bringing Fluffs back with her three kittens and reward you with a kitten of your own.
   
   
   
   

Kitten Care:

To make kittens grow into cats you can use balls of wool with them, have them chase and kill rats, pet them, and feed them. Once your kitten has grown into a cat, P2P users can take it to any Civilian in West Ardougne (assuming that you have done Plague City and Biohazard Quests to get in). They will give you 100 Death runes for your cat. Alternatively you can grow it into an Overgrown cat, Lazy cat, or Wily cat.

For more information check the Cat Care guide.