Jump in a pool (this isn’t an option for me, sadly.)
From my experience, there is no sure-fire, easily-enacted way to remain cool during hot days. It’s why I detest them. The easiest thing to do is run the AC during the peak of heat (usually late in the afternoon) so the house will cool down for the rest of the evening. We leave it running for a couple hours and then turn it off.
Fans are better than an AC for keeping cool throughout the day without running up any bills. Have two types: a large one that will circulate air throughout the room and a smaller one you can keep nearby and pointed just at you. We only run these in rooms occupied by bodies.
Other smaller things: a nice cold shower is lovely, wear minimal and loose clothing, stay hydrated with water, have a bottle of water you can mist your face with (you can purchase these cheap – mistymates aren’t worth the money), and you can never beat ice cold treats (I enjoy raspberry sorbet the most.)