During the current tax year (which started on 6 April) you can earn �6475 without paying any tax on it. (That assumes that you're not, for example, over 65 years old. Other exceptions are listed here:
http://www.hmrc.gov.uk/rates/it.htm )
That figure should be confirmed by your tax code, which will be on your pay slip. It should (unless you fall into one of the 'special' categories referred to in the above link) be 647L, although it might temporarily be different for a new employee.
�6475 per year is equal to �124.52 per week. For tax purposes a pay week runs from Monday to Sunday. So, up until last Sunday, you'll have been allowed to earn 3 times �124.52 = �373.56, without paying any tax on it. (The word 'earn', in that sentence includes things like Job Seeker's Allowance, which you might have been receiving prior to starting work).
So, if you've only just started work (for example last week), you'll have received some of the 'tax free allowance' from the previous two weeks..
If you never earn more than �124.52 per week, you'll never pay any income tax. If you earn more than that, you'll soon reach a point where you've used up any 'spare' tax-free allowance. Thereafter you'll pay tax, at 20%, on whatever you earn above �124.52. So, if you earn �150 every week, you'll be taxed on �150 - �124.52 = �25.48. 20% of that is �5.10, so that's all the tax that you'll pay.
Similarly, if you earn �200 every week, you'll be taxed on �200 - �124.52 = �75.48. 20% of that is �15.10 to pay in tax.
Those figures only show tax. You'll also have to pay National Insurance, at 11%, on your weekly earnings over �110. So, if you earn �150 per week, you'll pay �4.40. If you earn �200 per week, you'll pay �9.90.
Chris