Hi Katie! Turning the power off is definitely the most important. :)
Outside of that, there are a couple things to know with fans. First, most light boxes in ceilings are not designed to hold a fan. So it’s important to check and make sure your box is mounted properly to support the extra weight. If you’re replacing an old one, then I’m guessing you’re fine (though it doesn’t hurt to double check, in case the previous owner didn’t know what they were doing). Another thing to note is that you may have some extra wires, depending on the fan. You only need to worry about this if you’re hooking your fan to one switch, and the light on the fan to another. If you’re trying to do something like this, I would do some additional research and contact the fan company to make sure you do it the right way. If you’re not going to have them on separate switches, then you’ll connect the extra wire to your black wire from the fan, and connect both to the black wire in the box – though this may be different with each fan so you’ll want to check with the manufacturer to make sure. I hope that helps!