You can't do much better than to have a read of the P87 form and supporting guidance notes, at least as a starting point, both to be found here:
http://search2.hmrc.gov.uk/kb5/hmrc/forms/view.page?record=lNKqI3HRKkQ&formId=769
As regards the mileage, you can claim 45p per business mile for the first 10000 business miles per tax year, 25p per mile for excess, less amounts paid to you for mileage by the employer. You don't get the full amount back from HMRC at that rate of course, you simply get an allowance of this amount as a deduction from your taxable income. There are supplements for taking passengers on busines journeys.
A significant risk in relation to mileage is that what YOU regard as "business" mileage and what HMRC regard as "business" mileage may not coincide. If your employer pays for some miles and not others then I speculate that the risk of different interpretations here is heightened.