You need to have a look on the HMRC website to check that what you are doing really meets the threshold for self-employment. It's not unknown for employers to try and get round paying tax and employer's NI by claiming someone is self-employed when in fact they are not.
If you are definitely self-employed, your rates need to reflect the fact that you don't get holiday, sick pay etc so if this would normally be a minimum wage job, you need to be charging a good 30% more than that (I'm not suggesting it is a MW job, just using that as an example).
From there, it's about keeping careful track, invoicing, registering for a self-assessment tax return, filling it in, paying your tax from there.
You are allowed to earn a small amount (I think it's around £1k but don't quote me on that) from self employment without registering as self employed, but even if you earn under your personal tax threshold you still need to do a tax return. And think about voluntary NI payments if you don't meet the threshold for them, to protect your pension contributions.
It's actually not complicated - aware it doesn't sound like that - but there is an element of self-management and hassle so you have to work out if it's all worth it for you.