You can catch Wynaut on Mirage Island in Pokemon Ruby, Sapphire and Emerald.
In Fire Red or Leaf Green you must breed Wobbuffet while making it hold Lax Incense, to get a baby Wynaut's egg. To find a Wobbuffet you need to defeat the Elite 4 and enter Cerulean Cave.
In Pokémon Emerald, you can get a Wynaut egg from the lady in the sand near the hot spring in Lavaridge. Just leave it as one of your Pokémon until it hatches.