Its really easy
Read this:
http://www.hmrc.gov.uk/startingup/register.htm
I literally called them up (had to do it after my first day of starting), they then set up my NI contributions direct debit, which is something outrages at £2.20 per week

( class 2 for now but increases depending on income to class 4).
As I'm in construction, I'm CIS registered and 20% tax gets deducted by the company I'm working for ...most are CIS registered. They then give you a payment certificate which covers is proof that your tax has been paid. You'll need a UTR number for 20% payment and that can take anywhere between 3-7 weeks to come through. Until you get that your on 30& tax deduction.
I think that about covers most of it