For 40 years, my house had no central air conditioning. There were window units from time to time, but the original windows were narrow steel casements that weren't window-unit-friendly, plus there was the question of what to do with them in the winter. Window units are too heavy for a single woman to maneuver. I had a portable unit in my bedroom, but its little water tank would fill up by the middle of the night, turning it off.
How ever did I survive?
1. In the morning, go around and cover all of the windows, particularly any south or west facing ones. I had blinds, but curtains that are white on the outside would work too. While you are at it, close the windows. Leaving them open on a hot day just lets hot air in.
2. In the evening, go around and open all those windows. Depending on the window, you may be able to leave the blinds/curtains shut or only partly drawn.
3. A fan in every room. Lots of fans. Big floor models, little swiveling fans, maybe even an itty bitty fan for when you are sitting in one place for a while. Moving air doesn't actually do much for the ambient temperature, but it will make you feel better.
4. Speaking of fans, a whole house fan. I'm a little hesitant to recommend this because mine sounded like an airplane engine. Each summer, it took a while to get used to the noise, especially since it needed to be run at night. But it did do a very good job of drawing hot air out of the house, so that cooler night air could come in through those open windows.
5. Don't plan on doing much of anything at home during the afternoon. There is a reason why the siesta was invented. Alternatively, go out to air conditioned places. I got used to going to the movies by myself because many a summer weekend included a matinee movie.
6. Ice. In tall glasses with the beverage of your choice.
Incidentally, in winter, reverse the blind opening and shutting, opening during the day and closing everything up at night. (Leave the windows themselves closed, of course) South-facing windows can gather a lot
of solar heat.