Melting
The molecules in a solid, which are bound by inter-molecular forces, vibrate around their equilibrium position in a crystalline structure. During melting, the molecules gain energy to weaken the intermolecular attractive forces and increase the distance between the molecules (increasing their potential energy while keeping kinetic energy constant), thus acquiring the greater degree of freedom and disorder.
Image by: Markus Schweiss. Link: http://en.wikipedia.org/wiki/File:Kochendes_wasser02.jpg. Released under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Boiling
During boiling, the molecules need energy to overcome the intermolecular forces that hold them together and to increase the separation between the molecules. Some energy is also required to allow the vapour to expand against atmospheric pressure. The total energy required is the latent heat of vaporisation.
Evaporation is the change of state, from liquid to gas, that takes place at the surface of a liquid at any temperature.
