Well, it depends upon what it is that you want to do. It also varies by County, and by state. It can also be more strict within the limits of a city than it is out in the country, or more rural farming areas.
I have very large old oak trees on my property that I would definitely have to apply for a permit to remove. They are known as "grand trees" and are protected by a state law. But smaller, less ancient trees like palms, I can take out with no permission.
I would have to submit a design, and get a permit to build any sort of structure on my property. It also would have what are known as "setbacks" which means a house, garage, shed or stable would need to be a certain distance from my property boundary. I also must get a permit to build a fence, and there are restrictions as to how tall the fence can be, and how close to the road it may come.
Many people here in Florida and other parts of the US live in what are known as "deed restricted communities" which have many more rules and restrictions, such as what plants you can plant and where, what kind of fence you can erect, what cars can be parked in your driveway and even what color your mailbox can be. When you buy a property in one of these communities, you agree to abide by the strict rules and there are big fines for breaking them. It's mostly about keeping these neighborhoods looking nice, to regulate the property values. But it really does get out of hand in some places!
Our first requirement when we looked for a new home was "non-deed restricted". We have boats, hobby cars and a crazy gardener (me) that wants to plant one of every type of plant . . . couldn't live with restrictions. I have a sort of little botanical garden here on our property now.