Ionic solids have a crystal lattice of positive and negative ions. Ionic solids generally have high melting points, which can be explained by the fact that ionic bonds are hard to break. 
On the other hand, metals can be seen as an ordered network of positive ions that are packed closely together, and there is a "sea" of mobile valence electrons that can flow easily throughout the metallic crystal structure. (By the way, the presence of these mobile electrons explains why metals are such good conductors of electricity.) 
The melting points of metals varies widely on the periodic table. Cs melts at 28C, whereas tungsten melts at 3422C 
So what causes the trend in melting points for the alkali metals? A certain amount of energy is required to separate the metal atoms from each other. The larger the atom, the larger the distance between neighboring atoms in the metal crystal. The larger the distance, the easier it is to separate the atoms. 
Atomic size increases as you move down the group, because the energy level of the valence shell increases. The larger the atom, the lower the melting point.