The act of becoming self employed takes about 2 mins on the internet (HMRC site) and you'll also need to set up a DD (or pay the invoices) for class 2 NI payments which are somthing like £2.10 a week. Then at the tax year end you'll just have to say what your "profits" are (income less relevant expenses) on which your income tax and NI will be based – you'll also have to give details of your employemnt income the year too (if applicable).
If your income is likely to be low and relatively simple (eg handful of invoices a month) it should be pretty simple to keep your own records and do your tax return without paying an accountant to do it for you, also remember to save some cash to pay the tax man!
Therefore until you start earning any cash/work there's no real point registering as self employed, you can also just trade under your own name etc… as you won't be a registered company although can also use a company name if you so wish.
However all the above related to being a one man band sole trader as opposed to setting up a company or LLP which is discussed above. Also there are VAT consequences but believe your turnover needs to exceed about £70k.
Hope that helps clear the basics of SE…?!
