How does the molecular shape affect the boiling and melting point of a substance?

Well it depends on the type of intermolecular bonds the molecule has. More branched particles have LESS surface area compared to a straight chain molecule, hence experience less Van der Walls forces, lowering their boiling points. This is why secondary and tertiary alcohols have a lower boiling point, because of the weak VDW forces.... Other intermolecular forces include the Dipole moments and ofcourse the metallic bonding which depends on the valence electrons, known in high school is "sea of electrons"... But yea, basically less surface area, less forces, lower boiling point....

Generally the longer and more spread out the molecule the higher the boiling point and melting point vs. if it is bulkier. For example CH3CH2CH2CH3 will have a higher boiling point/melting point than (CH3)3CH.

Also, for melting point, the more symmetrical the compound, the higher the melting point.

Outside of just molecular shape:

Identity of atoms comes into play too- the bigger the atom the higher the bp/mp.

The biggest factor though is what type of forces molecules of the substance exert on one another- van der Waals, dipole-dipole or hydrogen bonding.

All ionic compounds are hard crystals at STP. They have high melting points. The reason is simply because the molecules have a high dipole moment, which means the molecules are adherent to each other, which means it takes a much higher temperature to pull them away from each other. Covalent compounds that have a low dipole moment, are loosely bound to each other. It doesn't take much heat energy to pull them apart. There are covalent compounds that have higher moments (not in the realm of ionic). SiO2 is one of polar covalent molecules that lend it a higher melting point.

due to change of state of the matter - from liquid to solid and vice versa

I've no idea what to say