You can purchase basic tools from the Nooklings, and you can craft better tools using recipes.
Getting Basic Tools
You can purchase tools from the Nooklings in the Resident Services Tent, but you should also ask Tom Nook for a DIY presentation so that you can start crafting your own tools. Your first recipe will be the flimsy fishing rod.
Redeem Miles for Better Tool Recipes
After you pay off your tent by paying 5000 miles to Tom Nook, you unlock Nook Miles+, which lets you redeem miles for more things from the Nook Stop Terminal in the Resident Services Tent. One of the new things you can get is the Pretty Good Tools Recipe Book. These are recipes for tools that will last longer before breaking.
Gather Materials to Make Tools
To make tools, you need materials. Read the gathering materials page for more information.
For a list of how long each type of tool lasts, visit the tool durability page.