Ok, so setting up a business is dead easy. Just have a browse on HMRC and give them a call if you have any questions, they are super helpful.
You also need insurance, if you don't already have some. Sometimes your training provider gives you an offer for a specific company, if not there are loads around.
Best of all, practise your new skills and enjoy what you do! If you're nervous and lacking a bit of confidence, don't worry, we've all been there!
I've got all of my current clients from word of mouth, family and friends, so I can't rly advice you on that. However I'd really recommend setting up a website, fb page, etc. with your information, as its great for ppl looking to contact you.
Pricing is a tough one, as it depends on what you're offering, what kind of clients you want to attract and what they are willing to pay. Have a look around what salons and other techs are charging in your area and place yourself where you want to be. Don't undercut and don't ve afraid to charge what you're worth, instead run an offer for a specific time or something.