To find out how to evolve Jigglypuff into Wigglytuff, read below.
According to Wigglytuff's Bulbapedia page, to evolve Jigglypuff it must be exposed to a Moon Stone.
To get one, head to either the Lake of Outrage or Dusty Bowl.
At the Lake Of Outrage near a Watt Trader are eight stones, check under them and there may be a Moon Stone
In the Dusty Bowl there will be some barren trees between a wheat field and a grassy rock, check under the stone there.