We use a separatory funnel. Polar and non-polar solvents generally do not mix.

Do you mean separate as in physically separate them in the lab, or do you mean separate as in “distinguish” ?

Most important difference for distinguishing polar solvents: look for O-H bonds, because they will have hydrogen bonding (O is much more electronegative than H and there will be a large partial negative charge on oxygen and a large partial positive charge on hydrogen). Second most important difference: look for bonds where there is a large electronegativity difference, such as the C=O in acetone and DMF, S=O in DMSO, CN in acetonitrile.

Very nonpolar solvents (hydrocarbons) only have C-H bonds.

The key measurement to look for is something called “dielectric constant” which is large for polar molecules and small for non polar molecules.