Drifloon is a "Ghost / Flying" type Pokémon featuring a balloon shape that appears only in the area in front of the "Turbine Plant" wind farm after you defeat "Team Galaxy". To make things even more difficult, Drifloon only appears on Fridays, so you only have one chance a week to meet him and try to catch him.
Steps
Part 1 of 2: Making Drifloon Appearance Possible
Step 1. In the normal course of the game, visit the "Turbine Plant" wind farm and defeat the "Team Galactic"
Shortly after defeating the first gym leader and earning the game's first medal, you will meet a girl on "Route 205", whose father has been taken hostage by "Team Galaxy" and is being held captive in the central "Turbine Plant". In order to capture Drifloon, you need to defeat "Team Galaxy" to free the "Turbine Plant" power plant.
Step 2. Defeat the "Team Galactic" members in front of the "Turbine Plant" wind farm
Dealing with the "Galaxy Recruit" should be pretty straightforward, but unfortunately, once defeated, it will block the door to the "Turbine Plant" powerhouse.
Step 3. To find another "Galaxy Recruit", you need to return to the town of Bloomfield
You will need to get a "Whirlwind" delivered by the members of "Team Galactic". In order to meet a "Galaxy Recruit", head south of the town of Giardinfiorito to get to the "Meadow in Bloom".
Step 4. Defeat the "Team Galaxy" recruits, then get the "Whirlwind"
In this battle you will have to face both recruits one after the other, so make sure your Pokémon team is in top form. If you face other opponents on a regular basis, this fight shouldn't be very difficult and you only need to defeat 3 Pokémon to achieve success.
Step 5. Defeat all "Team Galactic" members inside the "Turbine Plant" power plant
After obtaining the "Whirlwind", you can enter the wind farm and completely clear it of the presence of "Team Galassia". You will have to face two recruits and Commander Martes, who owns a Purugly at level 16, which will make the battle somewhat difficult. After defeating the commander, the girl will finally be able to hug her father again and will mention the presence of a "balloon shaped Pokémon". This is Drifloon.
Part 2 of 2: Spotting and Capturing Drifloon
Step 1. Return to the "Turbine Plant" wind farm on Friday
Drifloon appears in the area in front of the plant only on that day. If you faced and defeated "Team Galactic" on a Friday, you must wait until the following Friday to be able to spot Drifloon.
Make sure you arrive at the plant during the day, as Drifloon doesn't appear in the early morning or at night. You will have to visit the "Turbine Plant" between 10:00 and 20:00
Step 2. Do not try to change the Nintendo DS clock to manually set the date to Friday
Any such activity deactivates the timed events present in the game for 24 hours, thus also the appearance of Drifloon. The best thing to do is to set the date to Thursday and wait 24 hours for Drifloon to appear.
Step 3. Approach Drifloon and talk to him
Drifloon will appear in the game world in a very similar way to how it does in the case of Legendary Pokémon. Talking to him will start the fight.
Step 4. Lower Drifloon's health level
The Drifloon specimen you spot will be level 22, so if your Pokémon aren't strong enough, it will take some time to weaken it sufficiently. Drifloon is in trouble when it suffers "Ghost", "Rock", "Electric", "Ice" and "Dark" attacks; if you have the chance, then try to use this type of move to shorten the fight.
Step 5. When Drifloon's health has dropped sufficiently, use a Poké Ball
When Drifloon's health indicator turns red, you can start throwing Poké Balls in an attempt to catch him. To increase your chances of success, you can use advanced Poké Ball models. In any case, catching Drifloon shouldn't be too difficult even with normal ones.
Step 6. If you accidentally KO Drifloon or miss the time window it normally appears in, return to the wind farm the following Friday
Drifloon will appear as usual every Friday between 10:00 and 20:00.