When an air conditioner runs, it does two jobs. It lowers the temperature of the air, and it removes moisture from the air. To do the second one, the AC has to run for a while.
As the air passes over the evaporator coil, it encounters a very cold surface. Ideally, when the air passes over that cold surface, the air temperature drops about 20° F. In places where we have higher relative humidity in the summer, the other important process that happens when the air hits the coil is that the temperature of the coil is below the dew point of the air. As a result, water vapor condenses on the coil.
Here's the thing, though. Water vapor condenses on coils in oversized air conditioners, too, but you have to get enough condensation on the coil for the water to start dripping down into the pan below the coil. Even then, you're not there yet. You still have to get enough water in the pan for it drain to the outside.
Until the water that condenses actually makes it to the outside, you haven't really dehumidified the air. Why? Because that water on the coil can evaporate and get back into the air in the home. If you make the mistake of leaving your thermostat in the Fan-On position instead of Auto (Don't do that!), the water on the coil gets back into the air even quicker.
Oversized air conditioners don't run for a long time because they satisfy the cooling load quickly and then shut off. Properly sized air conditioners run longer, so if you want your air conditioner to dehumidify your home as well as cool it, don't let the HVAC contractor oversize it.
If you live in the desert, what I just said above doesn't matter to you. There's no water vapor to condense on the coil, and if there were, your dew point is probably close to absolute zero. (Well, OK, that might be a bit of an exaggeration.) The second reason definitely should matter to you, however. The thing that wears equipment out is starting up and shutting down. The more it happens, the shorter the life of the equipment.
When an air conditioner is oversized, it starts up and shuts down a lot more because it runs for only a short time to meet the thermostat setpoint. Then a few minutes later, it comes on again and runs for a short time. Over the course of a day, an oversized air conditioner can have a lot more start-ups and shut-downs than a properly sized air conditioner. That means you'll probably be repairing it more often and replacing it sooner.
People in the industry used to think you'd save money on your air conditioning bills with a properly sized air conditioner, but that thinking has changed. John Proctor wrote an article for Home Energy Magazine that shows only a small savings for the homeowner (but the utilities benefit by lower peak loads). You should save money on the upfront cost, though, because you're putting in a smaller AC. (As Proctor points out in his article, oversizing isn't always the worst problem, though. You have to be a subscriber to Home Energy Magazineto read the article, but it's well worth the read if you can get it.)
For new homes, use the full HVAC design process, which starts with Manual J, the heating and cooling load calculation protocol from the Air Conditioning Contractors of America, the trade association for AC contractors. For existing homes, the best way to do it is to see how long your current air conditioner runs when it's at the design conditions. Of course, you want to do this while your AC is still in good shape, not when it's on its last legs. If it runs for only 5 to 10 minutes before shutting off, it's definitely oversized. If your runtimes are over half an hour at design conditions, it's probably sized close to the actual cooling load.
If you're building a new home, remodeling an existing home, or just getting a new air conditioner in an existing home, ask your builder, remodeler, or HVAC contractor how they're planning to size the air conditioner. If they tell you they're basing it on the size of your house, don't let them do it. There's a lot more to it than square footage of conditioned floor area, and of course, I haven't touched at all on the capabilities of different types of equipment (single speed, fixed capacity, multi-stage, mini-splits...).