mafketis: umiem to zrobić - I know how to do it wiem, jak to zrobić - I know how to do it IIRC the difference for most speakers is the first implies that you've done it before, while the second doesn't (or maybe it's the other way around, my mind is a little muddied itself at the moment)
I think the easiest (though not perfect) way to understand the difference is to remember that 'wiem' expresses what you have in your mind while 'umiem' says about skills of your body (I know, it's often the same :-).
e.g. Wiem jak się jeĽdzi na rowerze (trzeba usi±¶ć na sidodełku, trzymać kierownicę i pedałować)
ale
nie umiem tego robić (bo mam problem z utrzymaniem równowagi)
Cinek
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