There are a number of routes, you'd probably set your self up as a sole trader and fill in a tax return to calculate the tax you need to pay. Assuming you're charging for your services, you'll keep track of your invoices and basically the tax will be worked out in a similar way to if you were employed. With being a sole trader I believe there is a small NI fee to pay. This is a simplification and others may give you more detail, but I don't think it needs to get more complex unless you have more complicated business affairs.
As self employed you invoice your customers, record the invoices you receive as part of your business and your tax is calculated when you do your tax return.
It's fairly simple if you don't earn over a certain amount (I think 15k but I can't remember exactly). You basically state your turnover and your outgoings leaving you with your net earnings. Over that threshold you have to provide detailed accounts.
As for better or worse off financially, it should work out the same in income tax, they just count it as an income.
The only difference as previously mentioned is the extra NI you pay if you earn over something like £4.5k I think (below that and you apply not to pay it).