If you are running your own business you need to register with HM Revenue and Customs within three months of starting your business, or you could pay a penalty.
You will pay tax on profit you make in excess of your personal allowance. You will normally be sent a Self Assessment tax return each year to enable you to do this. You may also have to pay National Insurance contributions. You may also need to register for VAT (although for a student in full-time education, this is very unlikely).
Because personal allowances are for all your income added together, you may find your income goes over the personal allowance if you have your own business and are also employed by someone else.
For more information on self-employment: