here is a link on how to do business in Connecticut http://www.ct.gov/ctportal/taxonomy/taxonomy.asp?DLN=27187&ctportalNav=%…. It is a government web site.
The one thing you need when you go into business for yourself is liability insurance. You can get great insurance through IDEA and can find out about it here at this web site. There are other insurances as well.
I would set up a business before I meet with a client (unless you act as an employee at a fitness club). As soon as a client pays for your services, you need to have a business under which you operate.
I understand that you itch to start training but you will be more respected by your clients and your peers when you go about it in the correct way. And do not be intimidated by dealing with government. Setting up a business does not have to be a grand affair, and the government employees are usually very helpful and want you to succeed.
I wish you good luck.
Call your State licensing board. Find out the requirements, if any, for licensing for fitness professionals. Set-up a 1-hour meeting with a business attorney (preferably with experience working with fitness professionals), at a minimum get your liability insurance and waiver forms in place before beginning to train. Taking the preliminary steps BEFORE you start training is worth it!