40Dropped by
getting one
The plain colored kites come off the slimes that drift in hanging from a Windy Balloon, and those only appear once the wind picks up. Kite drops in general work the same way: an enemy carrying one will not hand it over unless the day is windy or the wind is running hard.
flying it
On a Windy Day it climbs by itself. On a calm day you can still get one up, but only by running fast enough to fake the wind, and it fights you the whole time. Attack lets out line and raises it, open or activate reels it in, and reeling all the way down puts the kite away. Both the line and the kite pass straight through terrain, so a ceiling is not a problem. You can fly one from a mount or while flying, though your character sprite faces backwards while you do.
the buff it gives
Keeping a kite airborne builds High Spirits, and the timer climbs the longer it stays up until it caps out. While it runs you move faster, mine faster and place blocks faster, and you pick up a small luck bonus on top. That luck steps down in stages as the timer drains, so a buff you let run to the last few minutes is no longer helping your drop rolls even though the icon is still there. Put the kite back up before it gets that low.
the AFK trick
Leave a kite anywhere in your inventory, then stand still without moving, jumping or using anything for a minute. Your character pulls it out on its own. That is a free speed and luck buff on any AFK farm, and touching a movement key resets the clock. Since 1.4.5 you can also stake a kite into the ground as a permanent piece of scenery, where it rides several blocks above its anchor even on a dead calm day.