How do typical dipole-dipole forces differ from hydrogen bonding interactions?

Dipole-dipole forces occur when polar molecules are attracted to one another. Basically, if one atom on the molecule is more electronegative than the others, it will pull electrons toward itself, giving it a partial negative charge. Likewise, the atoms that have had electrons pulled away from it will have a partial positive charge. When two molecules of this compound come in contact with each other, the partial positive charge on one will be attracted to the partial negative charge on the other - this is a dipole-dipole force.

occur in molecules that have H-F, H-O, and H-N bonds. Basically, this strong intermolecular force is due to a strong dipole-dipole force as described above, plus the fact that the F, O, and N lone pairs are able to reach in closer to the hydrogen atom on another molecule.

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Simple, well organized with additional info here http://www.masterorganicchemistry.com/2010/10/01/how-intermolecular-forces-affect-boiling-points/