In the UK we have a simple system for normal employees called PAYE (pay as you earn). Basically the govt tells my employer what my tax code is and the employer sends part of my pay to the inland revenue every month before sending the rest to me.
Some things are tax deductible, like pension contributions, but as i'm in the employer's pension plan that's all calculated by them.
we do charitable contributions differently. Basically the charity gets to claim the tax not you, so if you donate money to a charity, you tick a box on a form and they get to ask the revenue for the tax you paid on that money.
that's all for normal employees. If you're self employed or have multiple income streams for several jobs, then you gotta do a tax return, which allows you to deduct some things.
my wife was a locum GP (she recently became salaried (i.e. directly employed)) and she got to claim mileage and depreciation on her car plus other things as well (her insurance was a big one). I felt sorry for her accountant given how bad she was at book keeping :)