Feeling comfortable in hot weather requires two things to happen together. The temperature and the relative humidity (RH) of the air must both be low enough to keep you from sweating. The lower the RH, the higher the temperature can be for you to feel comfortable. Think about dry heat in places, like Arizona, where 80 degrees can feel pretty comfortable, while that same temperature in Florida can be oppressive. That's because the RH in Arizona is probably about 20% while in Florida it's more like 90%. Lower the RH and you feel cooler right away.
There are two types of A/C: traditional, which removes moisture from the air, and evaporative cooling, used only in dry climates, which adds moisture while cooling. For the sake of this post, I'm only going to consider traditional A/C in humid climates, so if you live somewhere really dry, you can go enjoy planting your xeriscape garden (sniff) and leave us Southerners to discuss how to reduce the costs and environmental impacts of air conditioning in Orlando, Atlanta and other sweaty locales.
First, dress for the weather. If it's hot, dress lightly and keep the A/C set a little higher.
Second, turn on a fan. Air moving on your skin makes you feel cooler. But don't leave the fan running all day - only keep it on when you're sitting under it. Really, I'm not kidding, it only works if the air blows on your skin. When it doesn't the fan only adds heat to the room from the energy in the motor.
Third, control the humidity. The best way to do this is by sealing up the air leaks in your house, but that can be a big project for an HVAC contractor or roofer, although there are some DIY solutions. Even if you do a good job air sealing, you will still need to remove humidity somehow. If it isn't too hot, you might try using a stand alone or central dehumidifier. If you can get the RH below 50%, you can keep the temperature higher and still feel comfortable. If the RH is very high, then the temperature has to be much lower to feel comfortable. When your A/C runs it does two things: first it cools, and then it dehumidifies. If the A/C system is too big, it cools quickly and shuts off before it has a chance to take moisture out of the air. Smaller A/C systems usually work better than bigger ones because they run longer, which dries the air more.
Next, open the windows and doors when it's cool at night or in the morning. Then, before it gets too hot, close them all up, usually around mid-day or early afternoon. The house will stay cool, for a while, how long depends on how well insulated and air sealed the house is. When it gets too hot, turn on the A/C for a while, then, if it cools off enough after the sun goes down, open the windows and doors again and let the outside air cool off the house.
One last thing: sun shining in windows can really heat the place up. Close blinds on your south, east, and west windows to cut down on extra heat, or, better yet, install exterior shades or shade screens to cut out the heat before it even gets inside the house. When you dress lighter, open your windows, and use fans properly, you can use a lot less A/C without sacrificing comfort.