Well the difference is quite simple actually. ‘Know’ is the present tense while ‘knew’ is in the past.
If you are aware of something now, or you have the knowledge of something at the present moment, then you ‘know’ it . Some sentences :
Do you know who’s winning?
Yes I know who’s winning. Barcelona’s winning.
(because the match is on at the moment and this is your current knowledge.)
I know today’s temperature.
I know today’s time-table.
On the other hand, if you were aware of something in the past and that you had its knowledge ever before the present day or moment, then you knew that information. Let’s rephrase the same sentences into the past :
Yes, I knew Barcelona would win yesterday’s match.
I knew yesterday’s temperature.
I knew last Tuesday’s time-table.
There you have it! If you’re talking about the present, use ‘know’, else use ‘knew’ for sentences or speech in the past tense.