You could start out as an affiliate without a business and register one when you start to earn money.

However, some programs require you to have a business registered to join them.

Having a business can also be beneficial so you can deduct costs related to promoting your websites and affiliate offers.

See all questions and answers in my affiliate marketing FAQ

This question was answered by Aleksander Blomquist. He started out with affiliate marketing back in 2008. As of 2020, he is a full-time affiliate marketing guy with two businesses focusing on creating websites from scratch and monetizing them with affiliate programs.