You can craft items yourself using recipes at a workbench, and materials that you can gather.
You can get recipes in various ways. Talk to Tom Nook and ask for a DIY presentation to get a recipe. Sometimes your island residents will give you recipes when you talk to them. You can also buy them in the Resident Services Tent from Tommy. There is a chance that recipes will wash up on the beach in message bottles.
The DIY app is added to your NookPhone when you talk to Tom Nook in the Resident Services Tent and ask him to give a DIY presentation. You can use it to see the recipes that you have learned and check if you have enough materials.
Materials can be gathered around your island. Some can be picked up off of the ground, such as tree branches and stones. Some recipes use ingredients that need to be crafted using other recipes. For more information, see the Gathering Materials page.
To craft recipes, you need to use a DIY workbench. There is one in the Resident Services Tent, and there is also a recipe that lets you build your own workbench that you can place outside.