How to use a Slingshot
First off, you're going to need to buy a slingshot from Tom Nook's shop, at a price of 500 bells. When equipped, press or your character to fire a shot into the sky (the top screen).
If you see a present or something else fly across, run to the top border of your town, take out your slingshot and fire a pellet into the sky. If your aim is good enough, you may shoot down your target, and pick it up from the ground near where you are standing. Be careful if you are standing near the mouth of your river because if you shoot your present, it may fall and land into the river. Presents can contain furniture, other items, or foreign fruit. Each present contains one item. You may also realise that there is a present in the sky if you hear a sound that sounds like a strong wind blowing through.
Most of the confusion about presents is what times to hunt for them. Presents will only fly by during a certain period of time.
Presents will fly by the top screen between the hours of 8:00am and 4:00pm. Don't bother looking for them at any other times, as you won't find them. If you are within that block of time, the presents will randomly fly by on the top screen on any time ending in 4. Just follow the model XX:X4. Fill in the model with the numbers in your clock, and if there is an X4 in the minute slot, then there is a possibility that you may see a present.
To ease confusion further, here's a complete list of times you could see a present fly across the screen:
However, you have to remember, just because your clock has turned to a certain time on the chart, it doesn't mean that you will see one. It is totally random if you will see a present at a certain hour. However, if you're feeling down on your luck, there's an easy way to help see more presents fly by the screen.
The Four-Leaf Clover
The easy way to increase your luck is to wear a four leaf clover in your hair. When you see a clover patch on the ground, press on top of it to pluck it like a weed. Most of the time, it will simply disappear. However, if you're really lucky, it will contain a four leaf clover. Wear it as a headpiece in your hair, and it will give you good luck! The extra luck will increase the amount of presents you see come across the sky. This little accessory is a must-have for any serious present-hunter.
If you're not interested in doing anything else while you hunt for presents, equip your slingshot and wait at the top of your town, preferably by the Main Gate. Wait until the clock changes to one of the times listed in the above chart, and see if a present will fly across the screen. If you don't see one, wait another 10 minutes, and repeat this process. Keep doing this until you see a present fly across the screen. You'll know early on by a gust of wind that is easily audible above the background music. This sound comes along even when you are in your pause menu, so you'll never miss it, as long as your volume is up.
Position yourself a few steps in front of the present's current location and fire a pellet into the sky with . If it connects, the present will fall to the ground. Pick it up and open it to receive your reward. Just a quick warning: make sure not to shoot down the present above a river or waterfall, as it'll fall into the water, and you won't be able to recover it.
The Golden Slingshot
The most expert present hunters may wish to seek the rare Golden Slingshot. This exclusive tool has the same purpose as the standard slingshot, but instead, when the pellet reaches the top screen, it explodes into a V-shape, sending three shots flying into a spread out pattern. This makes it much easier to shoot down presents in the future.
Obtaining the Golden Slingshot is easy enough for those of you who stick with the endeavour of present hunting. Just shoot 15 presents out of the sky, and the sixteenth one will contain a Golden Slingshot!
Be on the lookout for other things that fly across the screen during the day, as well. You may be able to catch Pete the Mailbird on his daily rounds, and if you shoot him down, he may dish some interesting gossip on his co-workers and his girlfriend.
Gulliver also flies across the screen occasionally, usually on times ending on 32, but not always.