Burmy can be found by slathering honey on sweet honey trees (those large yellowish trees that you see every once in a while), and checking back in 12-24 hours. If the tree is shaking, there's a pokemon in it. This doesn't guarantee that you'll find a burmy, since other pokemon can show up, like cascoon, so find as many trees as you can, slather them all with honey and check back later. You can find honey by going to Floaroma Town, and going through the northwest gate. The guy in the flower fields sells honey.
Drifloon can be found after you've beaten Team Galactic at Valley Windworks east of Floaroma Town. It appears outside by the windmills only on Fridays.
Finneon can be found by fishing with a Good Rod at Iron Island, Fuego Ironworks, Valley Windworks, and Canalave City, and probably the routes between those towns.