Intermolecular forces are noncovalent forces between molecules.  There are a variety of these forces but the most common are:  dipole-dipole interactions, hydrogen bonding and van der Waals (or London) forces.  Of these, hydrogen bonds are the strongest followed by dipole-dipole interactions and finally, van der Waals forces.  Thus a sample of a substance capable of hydrogen bonding will have stronger forces between its molecules than those between the molecules of a substance which is only capable of van der Waals forces.  This means that it will take more energy to disrupt those forces between molecules and the first substance should have the higher boiling and melting points.

How do we know which type of intermolecular forces exist between the molecules of a given substance?  You must be able to figure out whether or not the molecules are polar (see the Molecular Polarity module).  If the molecule is polar, it has areas of partial positive and partial negative charges which can interact with the areas of partial negative and partial positive charges in a second molecule (since opposites are attracted to each other).  This type of force is called a dipole-dipole interaction.  Hydrogen bonds are a special type of dipole-dipole interaction but are about five times stronger and thus are considered to be a distinct intermolecular force.  Hydrogen bonds also involve the attraction of a partial positive atom in one molecule to a partial negative atom in a second molecule (and vice versa) but in this case the partial positive is a hydrogen atom which is VERY partial positive by virtue of the fact that it is covalently bonded to a small, electronegative atom (F, Cl, O, N).  This VERY partial positive hydrogen atom will be VERY strongly attracted to the partial negative atom in the second molecule thus making the strongest intermolecular force, the hydrogen bond.  If the molecule is nonpolar, then no dipole-dipole interactions or hydrogen bonding can occur and the only possible intermolecular force is the weak van der Waals force.  This force is sometimes called the induced dipole-induced dipole interaction since it involves the transient creation of an induced dipole within a nonpolar molecule due to the close proximity of the electron cloud of a second molecule.  As soon as the second molecule moves away, the induced dipole disappears.  While the induced dipole exists, that portion of the molecule is attracted to other molecules but as soon as the induced dipole disappears, the attraction also disappears.  Thus this type of force is weak and short-lived and occurs between nonpolar molecules.

Having been reminded of the three major types of intermolecular forces, you can now understand the solvent rule, "like dissolves like".  If you have a polar solute, you will want to choose a polar solvent so that the solvent can solvate (surround and form dipole-dipole interactions or hydrogen bonds) the solute molecules.  If you choose a nonpolar solvent, the polar solute molecules will be attracted to each other and not to the solvent molecules and no solvation will occur.  If, however, you have a nonpolar solute, you will want to choose a nonpolar solvent so that the solute and solvent molecules can interact by van der Waals interactions.  If you choose a polar solvent, the solvent molecules will be attracted to each other and not to the solute molecules and no solvation will occur.  In order for solvation to occur and a stable solution to exist, the solute and solvent molecules must be able to form intermolecular associations.  For this to occur, the solute and solvent molecules must be similar (both polar or both nonpolar); i.e., they must be "alike".