How does the potential energy of molecules increase during change of state, for example when ice melts into water or water to vapour?

This has to do with kinetic energy. When molecules of a substance bump into one another (when matter is heated), molecules accelerate, move more often at random within a given space, then spread farther apart.

Corresponding to increasing kinetic energy, the three states of matter are solid, liquid and gas (from less to greater). H20 is an example; the three states are ice, water, and steam.

Robert Fulton's invention of the steam engine functions by the principle of expansion of matter with heat, when molecules of water escape the liquid state to become become gas (at the boiling point).