The simplest thing to do is to register as self-employed. When it comes to filling in your tax return, you will fill in an Employment sheet (along with any details of tax you've paid by PAYE), and a Self-employment sheet.
You can do this all online and it will work out your tax for you.
Also, don't forget, when it comes to your first tax bill, you will be paying all of your tax (if you have any) for the previous tax year, plus half of your estimated tax bill for the following year (this would be in January), then the second half of your estimated bill in July, then the following January you make up the difference if you've paid too little, or get a rebate (if you want...you can leave it on account) if you've paid too much and so on.
If you want a rough idea of how much tax you are gonna be paying up front, speak to an accountant.