Ventilate properly. Old houses kept cool by having windows on all four sides of the house. This way, homeowners could open windows across from each other in the direction the breeze was blowing. Since most summer breezes blow from west to east, open the southwest and northeast windows to allow the breeze to blow in one window (windward) and be drawn out the other (leeward). Always open upper story windows to draw out the heat that rises and provide cool air to fall and replace it. If you can open the upper sash instead of the lower on the leeward side, the warmest air, not the coolest, will rush out of a room. Break the seal of old paint and replace window sash hardware if you can't open the top sash.
Use the superior qualities of an old house to your advantage. Thicker walls guard against the heat of the day and keep the house cool longer. Don't open windows until the arc of rising temperature inside the house passes the temperature outside. Open windows at night to let the cool air in and close them in the morning to keep it.
Follow advice given to anyone who wants to minimize energy use in the summer. Keep drapes closed to minimize solar heating. Install a dehumidifier because dry air feels cooler. Do tasks that require heavy work early in the morning or late in the afternoon. Everyone go out to dinner at the air-conditioned burger place while the house cools down in the late afternoon.
Install an attic fan and use it. Use ceiling fans to circulate but investigate the effects of a high-volume fan to push air up from the floor and circulate air. You can move it from room to room and it moves more air. Those oscillating fans and floor fans are generally useful only for small areas like your home office or kitchen. Box fans can be put in windows to help pull warm air out of rooms in the evening.
Try to shade the west side of the house with trees, awnings, pergolas or vines so that the sun doesn't bake the walls to keep things hot into the evening. We once had an 80-year-old brick house that you could cook an egg on for dinner because the concrete patio and brick wall were completely open to the afternoon sun. Dinners had to be served on the veranda that faced north, a more formal, but cooler, option.
Use the out-of-doors. Sit on the veranda with an iced tea in the late afternoon and wait for the kids to get home from the city pool. Invest in a gazebo with screening and put it under a tree for family dinners. Grill out whenever you can. You'll be enjoying a more leisurely-paced lifestyle and your kids will learn that watching the space station cross the sky at dusk is infinitely more entertaining than reruns of reality shows. If you live in the city, odds are that you have a porch or even a rooftop that can be adapted for cooking, dining and entertaining.
Improve the basement to use as a family room in warm weather. Stock your new family room with games and media including a weather radio for stormy nights.
If you must install air conditioning, investigate those systems with minimally obtrusive ductwork. Or room air conditioners can be placed in the rooms you use most. The others can be closed off for the summer like Grandmama did.