No need to remove the CPU cooling fan if it is working ok, if you do you are making more work for yourself + there is a risk of the CPU being pulled from it`s socket when the heatsink and cooling fan are removed, a good clean should be all that it needs, from memory the green plastic housing unclips and pivots backwards to allow access for cleaning, you can then follow my canned text below to help with the cleaning.
If the computer needs cleaning out, first remove the power cord from the wall and open up the case, take anti static precautions before touching anything inside, you can do this by touching a bare metal part of the case, remove the video card, blow out the slot and re-seat the card securely, do the same with the memory sticks, clean all internal fans, if you use canned compressed air do not let any fan spin freely this can damage them, use something like a clean lollipop stick to hold the fan still
Ensure that all internal connections are secure, re-assemble the computer, boot up and test.
Just a cautionary note - if you do use canned compressed air do not upend the can as it is possible for fluid to be emitted.
Offline now until around 10pm UK time as I have a night class.