Nonpolar molecules have no net dipoles. The most common nonpolar molecules are hydrocarbons. These are molecules made entirely of carbon and hydrogen atoms.
Nonpolar molecules are typically hydrophobic, meaning they do not mix well with water. This is because water is a polar molecule and tends to interact more strongly with other polar molecules. Hydrophobic molecules generally prefer to interact with each other instead of with water.
A polar solvent is best at dissolving polar solutes. This is because if a potential solute is non-polar, the solvent is more stable when clustering among itself. This is due to hydrogen bonds and dipole-dipole interaction generally being much more strong attractive forces than London dispersion, which is the only attractive force non-polar molecules can exhibit. It's important to understand that polar molecules also exhibit London dispersion, but that the effect of it is normally rendered insignificant by the much more powerful dipole-dipole interaction/hydrogen bonding. If a non-polar solution is added to a polar solvent, the non-polar solution will form either a separate layer or small bubble-looking clusters (called micelles). One way to force the two solutions to mix is by using a surfactant, which lowers the surface tension of a liquid. It works by attaching to a non-polar molecule with a long, non-polar chain of carbon and hydrogen atoms and attaching a polar molecule with its polar head.