Basically, think first about what type of structure the two substances are, and list all the types of forces/bonds there are between the particles in that substance, then work out the relative strengths of each one. Here are some common ones:
Hydrogen bonding vs Van der Waals
If one of the substances is polar and has hydrogen bonds (ie. a substance containing H with N, O or F), and the other ones don't. Common ones are HF (hydrogen) with HI/HBr/HCl (VdW), or maybe PH3 (VdW) with NH3 (hydrogen). Remember that all substances have Van der Waal forces within it; some have hydrogen bonds in addition to Van der Waals.
Van der Waals vs Van der Waals
If you have two substances, both which do not have hydrogen bonds, you're looking at the relative strengths of the Van der Waal forces. The more electrons you have, the stronger the VdW forces (because more electrons means that the temporary dipole is stronger). Thus, HI has a higher melting point than HBr, because iodide has more electrons than bromide.
Giant covalent structure vs simple molecular
For simple molecular structures (e.g. carbon dioxide), to melt it you only need to break the weak Van der Waal intermolecular force (you do not need to break the covalent intramolecular force). Giant covalent structures however do not have intermolecular forces (you don't really have molecules), so to melt it you need to break all the millions of covalent bonds, which takes huge amounts of energy. Thus structures like diamond, silicon and graphite have a higher melting point than simple molecular ones.
Group 1 metals vs Group 2 metals
Say you have Na and Mg, the mpt with Mg is higher, because the metallic bond is stronger. This is because there are two outer shell electrons that are delocalised and available for bonding, whereas with Na+ you only have one electron. Also the Mg2+ cation is smaller than the Na+ cation so that makes the bond stronger as well.
Ionic vs whatever
Ionic things like sodium chloride are usually held in a tight lattice, held together by strong forces of electrostatic attraction between the two oppositely charged ions. These ionic bonds are very strong so needs a larger amount of energy to overcome, than with say simple molecular structures. If you have to compare between ionic substances, think about the relative strengths of the ionic bonds: ionic bonds are stronger if the charge is higher (e.g. ionic bond between 2+ and 2- is stronger than 1+ and 1-) and if the ionic radii is smaller (bond length shorter, closer to nucleus etc). So MgCl is stronger than NaCl so MgCl has higher mpt.
I may have forgotten a few but those are the main examples you'll need. Hope that helps.