Covalent bonds occur between atoms that share their electrons with each other. This can occur only when the atoms have similar electronegativities (that is, a desire for electrons), because otherwise, there is a significant difference causing one atom to "steal" the other's electrons (making an ionic bond).
So, covalent bonds are generally made between two elements that have a similar electronegativity. As a periodic trend, the electronegativity of an element is affected by the distance of its valence electrons (you'll probably cover that with VSEPR theory) from the nucleus, and the number of electrons. Starting with fluorine as the most electronegative, electronegativity decreases as it moves down and left on the periodic table, reaching cesium, the least electronegative element. So generally, when two elements are very close together on the periodic table, they tend to form covalent bonds.
Remember that ionic and covalent bonds are two ends of a spectrum. We never really have a truly ionic or truly covalent bond. Rather, there are subdivisions, like polar covalent, which are based on the electronegativity difference and describe the degree to which a bond exhibits either covalent or ionic properties.
