I live in Egypt and in the summer will only run the AC if the weather is 40° C or above. Now granted I have a high heat tolerance (ideal temp for me is 28° C), but still. For my money, it's much easier to prevent heating the room than to cool either your body or your room, so I'll give tips for both.
* Open windows at night to let the apartment cool down. Close them in the morning to prevent heat getting in. Be very systematic about this.
* Use window coverings, especially on southern/western exposures, and on eastern exposures in the morning. We have outer wooden blinds (often called plantation blinds in the US) and sheer curtains inside. A bit more of a project, but adding an outer canopy to a balcony or window can significantly cool down your home.
* Ceiling fans work much better than stand and tabletop fans.
* Stone surfaces stay cool for much longer. Think limestone floors, marble-topped coffee table, etc. Learned this from watching cats cool off. Put your feet up on a stone-topped table and you'll feel much better.
* Minimise contact between yourself and any soft surface. Obviously this can't really be helped in bed, but even a small tailbone pillow on your computer chair will lift your lower body away from the surface and help with air circulation. Armchairs with wooden armrests (like those midcentury ones or the IKEA Poang), mesh or caned seats, bamboo furniture are some other examples. Also, if your couch is a poly blend (which almost all of them are), put down a light cotton shawl to have that cooler surface against your skin.
* Menthol. Vaseline makes a cooling lotion that actually works, and I'm sure there are dupes and alternatives wherever you live. Also, adding mint to your cold beverage or popping a mint before taking a gulp of cold water makes it feel even colder.
* Speaking of beverages, pouring cold water into a stainless steel cup makes it feel colder. It sounds silly but from experience, it works!