I would like to get into professional photography. How should I begin?

I have a Nikon D60 camera and nothing else.

What do I need to purchase or do in order to have a successful photography business? Are there any classes I have to take? What is recommended? Any advice is appreciated.

Cart goes after the horse, not before it. Stop thinking about owning and operating a business for about the next 3-5 years. Study everything you can about photography. Decide what you enjoy shooting most and learn everything from lighting, composition, posing (if need be), what lenses are best for those subjects, etc.

If you have a kit lens then learn from that and work your way up using that for practice. If you're interested in doing portraits, consider a 50mm or 85mm lens and learn everything you can about how to photograph people. Learn about model releases and how they're useful when working with people.

Take a few years to really learn how to shoot well and if/when you decide you're capable to take on paying clients then go for it. In the meantime, don't even think about starting a business just yet.

1.figure out WHAT you want to shoot. What market you are going for.

2. Create a portfolio of 10-12 exceptional images in this category.

3. Get a website to showcase this portfolio.

4. Figure out if you are going to be a Sole-Proprietorship, Corp., S-corp. Or LLC. And get that filed.

5. Get your federal EIN.

6. File for your state resale/tax license

7. If required file for a DBA in your county.

8. Start advertising and marketing

Stuff you would probably nee: A tripod, perhaps a DLSR or new lenses. Photoshop, or other editing softwares.

Try gaining more experience by taking lot more pictures, exploring new styles. There are no classes you HAVE to take, but it is best if you take one. Honestly, having photograph as one job, won't earn lots of money, so try getting photography as a second job/hobby. You don't need to be a professional to be a good photographer.

Buying a book for photography, taking a class, or doing some kind of project can work. Maybe doing a photography project where to take a different picture each day. Ex:

Day 1: A pretty plant or flower
Day 2: Your favorite food
Day 3: Your best friend.etc

"professional photography"?

Doing what sort of photography.

Sports
fashion
weddings
portraits
kids
photojournalism
wildlife
etc etc

If you want your own business then take business and marketing courses.
Sort out what your speciality will be and learn that for the next few years until you become good enough that people are willing to pay you for your services.

If I bought a frying pan, what else would I need to open a successful restaurant?

You are getting way ahead of yourself. It honestly is going to take $20, 000 or more to get a photography business started.