From here, scroll down to the bottom of the list, and you'll find a tile labeled "???? Android Easter Egg." Long-press this tile, then drag it up into the dark gray area at the top of this menu. Once you drop it in place, the Easter egg tile will be accessible amongst your regular Quick Settings toggles.
Step 3: Pick a Treat to Lure a Feline Friend
Next, expand your Quick Settings menu again, then tap the "Empty Dish" icon. From here, you'll be prompted to pick a snack that will hopefully lure in a cat, and the options are Bits, Fish, Chicken, or Treat. When you select one of these, the Easter egg tile will display the treat you chose.
Step 4: Catch a Cat & Share It
For now, just leave the Quick Settings tile alone, as this is basically cat bait. Eventually, though, you'll receive a notification that says "A cat is here"—just tap this to view your new feline friend. It may take a few hours for your treat to lure in a cat, but once you've nabbed one, you can long-press the smaller icon, then tap the share icon to save a bigger copy, or to send it to a friend through any compatible service.
Once you catch a cat, the Quick Settings tile will reset to say "Empty Dish" again, so you can repeat this same process to catch more cats. If the numbers are any indication (Cat #106 is the one I caught), there are hundreds of unique cats to catch—more than double in Neko Atsume. We have no idea what could happen if you catch them all, but judging by the rest of this crazy Easter egg game, it would definitely be something off the wall.