Start here
https://online.hmrc.gov.uk/registration/newbusiness/introduction You can do it all online.
You need to keep proper books so that you have a record of your income, expenditure and overheads. You also need to choose an accounting date (up to 15 months after you start, most people pick one year after). With an eBay business, your income is the total paid for things you sell, your expenditure is the cost of acquiring the things you sell and your overheads include eBay and PayPal fees, computer costs etc. On your accounting date, you calculate your net profit and you pay tax on that. You declare your profits - as well as your salary and the tax deducted from it - on a self-assessment return (which you can also do online). The tax calculation is to take your salary plus profits, deduct your personal allowance, calculate the total tax, then deduct what you have already paid under PAYE. NI is more complicated. There's a flat rate paid by self-employed people but you may get some back if you've paid enough on your salary.
A session with an accountant will set you in the right direction and should pay for itself in tax saving hints.