To be able to pick up treasures from the ground, you need to have the shovel and look out for a star-like symbol on the ground. Once you do, start digging and you will receive a treasure. Below are the different types of treasures and some specifics regarding treasure hunting.
These are blue, round objects that you need to bring to Blathers at the Town Museum to become valuable. As mentioned multiple times, always donate the first kind of any type that you have acquired to add completion to the collection. Take note that there are skeletons Fossils that are worth more than regular fossils. Also, skeleton fossils are several pieces that you need to collect to be able to complete the whole fossil istelf.
A maximum of up to 3 Fossils can be found per day, although some may not appear as easily if blocked by objects, such as trees. Weeds and patterns also lower the probability of new fossils showing up as they replace the chance of a fossil spawning.
Pitfall Seeds
Round, white objects bearing a red symbol. Walking right into a digging area with a pitfall seed in it will make you fall down below, in which case you need to press A to escape. These are used to trap other villagers if you like to.
Small, brown objects that sometimes show up instead of Fossils when you try to dig out. These can be sold for 828 bells and can be put as display in your home, generating soothing, beautiful musical sounds.
Present Balloons
While walking you may sometimes hear wind blowing and if you look up there will be a balloon flying above that has a gift attached to it. These are called present balloons. Equip the slingshot if this happens and run up to the northernmost point of town. Wait for the balloon to fly over and shoot it. If you miss, just run up north again and wait, then keep firing away until you hit it. Make sure you don't hit it above water or you might lose it once it falls down. Patterns will also be troublesome as they will take up the space of the present when it falls down, making it disappear.
A successful hit will guarantee a gift falling down in the northern point of your town. These balloons will fly above the town everyday from 10AM to 4PM. After shooting down 15 balloons, the next balloon will be orange-colored and will hold the Golden Slingshot. Once acquired, this will shoot out 3 stones making present-balloon shooting much more easier.
Gulliver's UFO
Instead of the usual present balloons, a UFO may hover above sometimes. Shooting it down using the slingshot will drop UFO parts in the ground. Pick up all of the parts and return them to Gulliver who is residing inside the crashed UFO ship.