Not sure what your fan is but mine are create a breeze. The screen fits really tight. There is a place on the screen frame that has an indention. I take a screwdriver and pry it down from the fan. Fingernails are not strong enough. Hard to get the correct angle but that's what I do. Hope this is helpful.
There are two screws one on each side in the center of the screen rim. Remove them. If your screen is like my bathroom fan you will then need to remove the entire rim. It's not an easy screen to get to. The screen does not remove like a fantastic fan or Maxx air