Budget-conscious consumers are always looking for ways to reduce their utility bills, and depending on where they live and what time of year it is, the bulk of those monthly bills usually cover the cost of climate control: heat in the winter, air conditioning in summer.
So in winter you find ways to make do with less heat - wear a sweater, find and block any drafts, open the curtains on sunny days for passive solar heating, things like that. However (unless you live someplace like Hawaii, or the southernmost parts of Florida or Texas), nobody would seriously advise you "Just stop using heat at all! Deal with a little chill. Buck up and live with mild discomfort. Harrumph; you're so spoiled." That's because everyone knows: once outside temperatures drop below a certain point, heat isn't a luxury but a necessity.
Yet where air conditioning is concerned, there is still a widespread idea that it's merely a luxury, not a necessity: "Deal with a little sweat. Live with mild discomfort. Go suck an ice cube - that's advice, not an insult." (Personal disclaimer: as a current resident of the humid Southeast, I generally take a "No A/C; deal with a little sweat" attitude until around 90 degrees; once it's that hot inside my house, I shut the windows and turn on the air conditioning.)
It's true that humans lived in hot climates for thousands of years before anyone had air conditioning, or even electricity to power a fan or produce ice cubes in a heat wave.
But historical people, for all their other problems, at least never had to deal with the horrors of modern architecture. For example: I live in a townhouse row apartment, identical to the other dozen or so other units in my building-all of which have a gigantic sliding-glass back door (read: an entire wall made of glass), facing due west for maximum summer sun exposure.
At least my glass door/wall can open to let in outside air; many modern buildings, especially office, business and retail establishments, have enormous glass window/walls that can never open at all, so air-conditioning is the only possible means of the lowering the inside temperature, even if outside temps are pleasant or downright chilly.
Another variable is not merely your house or apartment, but its immediate surroundings - do you have trees or anything else making shade? Even if you only have grass or short shrubs, a building surrounded by plant growth will stay cooler than one surrounded by concrete or asphalt pavement.
And of course, even if you have shade trees, decent insulation, proper windows, high ceilings and every other stay-cool architectural advantage, it still might be too risky for you to try going without air conditioning, if (among other things) you or anyone in your family suffers from health problems, or you live with someone very old or very young.
Lots of fans
Ceiling fans can help cool and heat.
But if you and everyone in your household enjoys generally good health, it is indeed possible to stay cool without air conditioning through all but the worst heat waves - provided you have a decently insulated house, proper windows and enough electric fans.
The first thing to remember is: simply having "a fan," singular, isn't enough. You'll need several, depending on how many windows you have, how large your rooms are, and other factors.
Also remember that, unlike air conditioning, fans do not actually make the air cooler - if anything, the movement of the blades and engine most likely generate a little heat of their own. But a fan can help cool you down, by assisting your biological cooldown mechanisms: in other words, making your sweat evaporate faster.
Here's a thumbnail physics lesson: when liquid water turns into gaseous water vapor, it also takes heat away with it. That's why humans perspire: when it's hot, water collects on your skin and the water removes excess body heat as it evaporates.
Unfortunately, that's also why hot humid weather is so much worse than hot dry weather: once the humidity reaches a certain point, water cannot evaporate, in which case perspiration backfires: instead of evaporating and cooling you down, it lingers on your skin and only makes you feel hotter (not to mention slimy, stinky and in need of a shower).
So that's one use of a fan: not cooling the air, but cooling you. Though fans can indeed cool the air inside your house - if you're fortunate enough to live in an area where, no matter how miserably hot it is during the day, at least the nights get cool.
Once the air cools down you want several fans set up in your windows to draw in cool air from the outside. However, you also want at least one window with a fan blowing outwards, to remove hot, stale air from inside your house. Ideally you want the fans blowing in the same direction as any outdoor breezes; of course, that ultimately depends on where your windows are relative to the wind.
Conventional wisdom says that during the hot sunny hours, you should close and cover your windows to keep the cool air inside; don't open a window unless the outside air as cool, or cooler, than it is indoors. This definitely works, but I've also discovered that when the outside temperature is only slightly too warm (say, high 80s rather than low 100s, though your preferences may vary), the inside of my house stays a bit cooler when I keep a couple of windows open and a small fan in the window blowing out, against the hot air.
Then again, I work out of a small office room containing one adult human and lots of electronics, all generating various amounts of heat in need of displacement. If you have a large and mostly empty interior space filled with cool air, you're better off keeping it sealed against the hot air outside.
Of course you already know to "stay hydrated," but you might not know how easy it is to become dehydrated without even realizing it. Don't wait until you're thirsty to get a drink; keep sipping ice water all throughout the day. You could also drink cold soda or other forms of sugar water, but plain ice water is cheaper, healthier and calorie-free.
Perhaps the most important thing to remember (especially if you're reducing your A/C use primarily for financial concerns - "I can't afford high electric bills") is this: don't push it too far. Deal with a little sweat and discomfort, sure - but too much heat can kill you sure as freezing to death.
When your local meteorologists start talking about "heat waves" and your city is operating emergency cooldown shelters and urging people to check on their elderly neighbors, that is not the time to "tough it out" or "sweat through it" in hopes of knocking a few bucks off your electricity bill.