Find and approach a tameable cat in Minecraft
Ensure you have raw fish or cooked salmon in your inventory
Hold the fish in your hand
Right-click or use interact on the cat to feed it
Wait for the hearts/angry particles to confirm the cat is feeding
Repeat feeding until the cat becomes tamed
After taming, the cat will follow you and have a collar/ownership mark
If the cat becomes wild again, repeat feeding to tame it again
If the cat is a stray cat, repeat the feeding process until it tames