Just realized that the Heatwave thread didn't have much in the way of methods to keep cool, so I guess to start:
1) Obviously, if you can afford the water costs, cold baths / showers every now and then will help. Even if you don't like cold baths normally, you will in hot weather.
1a) If cold showers / baths really aren't your thing, or you have something (like arthritis) which make it a monkey's paw solution, consider just a foot bath instead. It won't chill you as thoroughly, but it's at least something. Also it will make humidity less a concern later, at least.
1b) In theory, if blasting enough cold water (or you have enough ice to spare with putting some in an ice water-filled bath), you can combine this with #2.
2) Speaking of water and cold, if you have a non-oscillating fan, some (rather large) bowls filled with ice set in front of the fan can help. Unless you can crank out ice like something awful it's not an indefinite solution (generally only buying a couple hours of relief at a time), but some relief is better than none. Though if ice isn't a concern (especially if you can keep it going for a while with pre-existing fridge / freezer / cooler space; or have access to a grocery store with ice bags / dry ice), try to set up a circulation in the rooms you most intend to occupy. Even without buckets, large pots, or so-on you can usually rely on at least two rooms in any given abode (Kitchen, Bathroom) to have something you can plug, fill with ice water, and put a fan relatively safely in (most kitchen sinks have counters, and most bathrooms should have somewhere to put a fan that has no risk of tipping into the water).
3) Use strips of fabric (rags, old clothes, whatever) soaked in cold water (potentially even refrigerate or - for quick results - partially freeze for greater chill) and apply as necessary. Usually for something like this you're going to apply it somewhere like around the back of the neck, on the forehead (particularly if lying down), etcetera.
4) Minimize the area within the house in which you're attempting to chill. Generally, even a single bedroom apartment is going to be a tall order to self-AC. If you have rooms that're going to be continuously exposed to sunlight and you don't need to be in them, close them off unless their air flow is absolutely necessary to maintain a current. Alternatively, if you have large chunks that can't be sealed off (and no way to impromptu seal them with things like hung blankets or the like), pick a small area and do what you can to make it as comfortable for you as possible.
5) Higher is usually worse, lower is usually better. Basement floors are much more chill to relax in than first story which is much more chill than second. Again, doesn't apply in many places, but for those it does it can be helpful if not aware of as much (if usually in a rather consistent environment, for example).
6) Laptops, Desktop PCs, certain consoles. Anything that can produce moderate to significant amounts of heat? Try not to use them. I doubt I need to mention oven / stove-top cooking, but a lot of people forget just how much heat one of the above can dump into your home if you aren't paying attention. Or, alternatively, how fast they can heat up if the environment doesn't provide its own cooling for them.
It's not a perfect list, and in general is only really short-term (if your house gets above a certain point, none of the above will especially help: Bite the bullet and go to a family member, friends, or business wherein it is below that point), but they can make things a little less insufferable. This coming from somebody in a top story apartment who has had to deal with 95°F+ days outside with their AC busted.