Turn your computer off, and put on an Anti-static wrist strap to make sure you don't accidentally damage your computer.
Look for some screws near the back of your case (possibly thumb screws). Unscrew them, and take the side panel(s) off of your computer case. Use some compressed air and possibly a pair of tweezers to remove as much dust as possible from the inside of your computer case. Be careful to not touch or scrape any of the components inside with the tweezers.
Removing as much dirt and dust as possible will likely not make the computer any faster, but it should make it quieter.
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Your fan is coming on in an attempt to cool your machine. Overheating can cause the processor to overheat and slow down. A faulty fan can contribute to overheating. After cleaning the machine as Taylor recommended, if the fan is still making noise it may need to be replaced. Running your machine without the fan can destroy it. We may have a guide for doing this but need to know the model and make of your PC.