Here are a few links I found useful, when signing up as a self-employed sole-trader.
It seems the UKRC is a mass of information but the search engine it uses is useless, unless you know the exact name of the form you are after, so hopefully this list of links will save you time in the future.
So first off the HMRC website has the basic info on what to do first - https://www.gov.uk/working-for-yourself advice from a couple of financial bods told me the form used to be a self-assessment and a separate self-employment one, now the form is a single dual-use one, called CWF1, however you can now do this online - Complete an online registration form for Self Assessment
If you are in full time employment on a payroll and you want to do extra work as freelance, you still have to sign up as self employed.
According to HMRC you can be employed and self employed at the same time.
So, once you’re registered, how on earth do you figure out paying the correct tax and/or NIC? Well, here a useful tool from the TUC to get you going - https://worksmart.org.uk/tools/tax-calculator
Here’s some useful links to get you thinking about what you want to do for self-employment work…
Checklist from Prospects - https://www.prospects.ac.uk/jobs-and-work-experience/self-employment
Freelance UK - http://www.freelanceuk.com/
Citizen Advice Beureau FAQ - https://www.citizensadvice.org.uk/work/self-employed-or-looking-for-work/self-employment-checklist
Freelancer Start-up Guide - http://www.bytestart.co.uk/content/24/24_6/freelancer-startup-guide.shtml
Interestingly the most common sectors for self-employment is IT, Visual Arts, Health and Excersize, Media, Performing arts, and Business and Law.