A couple of questions.
What CPU do you have?
Have you taken the cooler off yet? It sounds like you haven’t, and that’s a pretty important first step. I recommend running the computer for a little bit to get the cpu up to temperature to soften the thermal paste before trying to remove it. Most CPU coolers are either screwed or latched in place.
Once the cooler is off what exactly you’re looking at will vary slightly between which CPU socket you have. Most have a little round rod/lever that runs along the side of the socket that will need to be lifted before the cpu can be removed. It should come out easily
Or even 🕖