Animal Crossing: New Horizons allows you to survive on a fairly healthy diet, even if you are on a desert island. Fruits will be something that you will use regularly during the game, but if you want to expand your food horizons, you will have to go beyond your own small island.
Your starting island will only have one type of fruit, which will be quite abundant and will grow on trees all over the island. You can shake the tree by hitting A near it, or hit it with an ax, to drop the fruit, pick it by pressing Y.
There are other types of fruit in the game, but they will be on other islands. To get your hands on them, you will need to visit friends and trade with them to get the different fruits.
After a few days on the island, your character's mom will send you a gift containing a different type of fruit. In our game, we started with Peaches on the Island, and the present one contained Pears.
The last way to get a different kind of fruit is by going to a Mystery Island using a Nook Miles ticket. A Nook Miles ticket can be purchased at the kiosk in the Resident Services Tent for 3000 Nook Mile. You will also get one for free from Tom Nook upon completion of the tasks he gives you. The Mystery Island will contain coconut palms, and you can harvest the coconuts and bring them back to your island.
When you get the different types of fruit, you can use a shovel to dig a hole and then plant the fruit to get your own tree and a steady supply of new fruit.