How to change the way how LaTeX gives numbers to chapters, sections...

The best way is to use a renewcommand.
For instance :
\renewcommand\thesection{\arabic{part}.\arabic{chapter}.\arabic{section}}

gives 1.1.1 numbers to sections while :
\renewcommand\thesection{\arabic{section}}

will only display the section number of the given section without chapter or part information.

this can be used to redefine :
thechapter, thesection, thesubsection, and so on...