If you have a dishwasher, the order in which you load the dishes doesn't matter much. But if you're hand-washing them, it's important to do so in an efficient way.
Start by rinsing off all the food scraps and grease from each dish. This will make washing them much easier and prevent clogs in your sink. Then, fill up your sink with hot water and dish soap and start with the glasses. Wash these first since they're typically the cleanest items. Move on to plates next, then bowls, silverware, and finally pots and pans.
As you're washing each item, stack it on a drying rack or towel nearby. Once everything is clean, put away the plates and bowls first, followed by the silverware and glassware. Pots and pans can go last since they often need to air dry completely before being stored away.