When you mix polar and non polar molecules, polar molecules do stick to non polar molecules
. This is because when a polar molecule A goes close to a non polar molecule B, B's electron cloud gets polarized and it forms a temporary dipole. This dipole exists as long as A is in the vicinity and they attract each other.
Of course, this attraction is weaker compared to that between two permanently polar molecules but there is considerable attraction between B and A.
To help you understand better, think about this experiment. You have rubbed a comb in you hair and tried to attract pieces of paper with it right (If you haven't, try it now!
). What happen here is there is charge transfer from your hair to the comb. Now when you bring this comb towards the paper piece, the neutral paper piece gets polarized and thus gets attracted to the comb. This paper when brought close to another piece induces a dipole moment in the new one too and thus they are attracted.
This is similar to what happen on the molecular basis. The induced dipole is capable inducing a dipole in another molecule (and hence attracting) of the same kind.