As James says, the personal allowance this year is £6475 unless you are over 65 (in which case you look very young for your age!) This applies to total earnings during the 2010/2011 tax year, which runs from 6 April 2010 to 5 April 2011. The personal allowance for the 2011/2012 tax year has been set at £7425, a larger than usual increase; these allowance are normally increased each year more or less in line with inflation.
To make life easier, the allowance is spread throughout the year, so if you are weekly paid the 1/52 of the allowance will be available each wee, so this year you would have tax deducted (if you are on PAYE) on weekly earnings above £124.52; if you are monthly paid then the tax-free figure is £539.58. Unless you are quite highly paid, the tax due will be 20% of your earnings that lie above that personal allowance.
A couple of final points. If you are new in the jobs market then you may not have a tax code, and in this and some other cases employers have to deduct tax from your full earnings, without giving you any tax-free amount. Don't worry if this happens, because (unless the tax office or your employer makes a mistake, which can happen) it will all be put right during or at the end of the tax year. If you think that an error might have occurred, to talk to your employer or your tax office or, of course, post a question on this site.
Secondly, don't forget National Insurance. This is another tax, which is charged on weekly earnings above £110 this tax year (£139 next tax year), at a rate of 11% on everything above that limit.
As with all tax answers, your individual circumstances may bring different results - this answer, for example, is a guide for a relatively young, employed person (as opposed to self-employed) who is not in receipt of taxable benefits. | 12.22.10 @ 18:50