Step 1: Using the periodic table, find how many electrons are in the outer shell of the central atom. Step 2: Add one electron for every other atom that the central atom is bound to. Step 3: Look at the net charge on the molecule add n electrons for a molecule with charge= -n. Step 4: Divide by 2 to give the number of electron pairs around the central atom. Step 5: Find the arrangement of electron pairs which minimises their repulsion.
Using water as an example (H2O). Oxygen is in group 6 so start with 6 electrons. It has 2 Hydrogen atoms bound so +2 electrons. It has no net charge. Total electrons = 6+2 = 8 electrons. So electron pairs = 8/2 = 4 electron pairs around the central oxygen atom. This means the shape of the molecule will be based on a tetrahedral arrangement of electron pairs ( bond angle = 109.5), however only two of these pairs are covalent bonds, the other two are lone pairs so the molecule has a bent shape. Lone pair - Lone pair repulsion is greater than bonding pair repulsion so the bond angle is actually = 104.5