If this is your first time, get hold of a can of compressed air specifically developed for cleaning computers and not from your garage compressor. Canned air is moisture free to avoid contaminating the electronics. Hold the Power supply for a few minutes while you take a look inside to admire the parts (this discharges any static electricity from you) Check all vents for the internal fans along with the one for the power supply. If they are dirty try to blow air through them to remove all dust and debris from all visible parts. If the said computer is visually dusty, you might want to do this outside the house. Also pay close attention to the CPU and blow air onto the fan and heat sink. Once you are satisfied and all visible dust and fido hairs are gone, you can reverse the process and take the camera shots to re-connect all the cables and chords that you took out and boot up. A clean computer runs cooler and more efficiently, besides too much dust on any of the internal components can lead to parts failure due to the insulating properties of dust.