The ionic bond is where an atom takes one valence electron from the other. This will give one atom a positive formal charge and the other a negative formal charge. The two atoms stay together because of the electrostatic attraction of the plus and minus charges.
The covalent bond is one in which two atoms share two electrons. They do this to fill their valence shells.
The way to find whether a bond is ionic or covalent is to look how far apart the two atoms forming the bonds are in the periodic table. If one atom is of the far left (Group 1 or 2) and the other is on the far right (Group 5, 6, or 7), then the atoms will have large differences in EN and will form an ionic bond. Most other pairs of atoms are close enough in EN to form covalent bonds. For example, any two atoms in the main group elements (Groups 3, 4, 5, 6, 7), will usually form a covalent bond. Remember to treat hydrogen like a Group 3 element as its EN is closest to boron.