What cpu are you using? What socket?
First of all you want to remove the heatsink covering the CPU, you can use google on how to remove it. Once that's out of the way you want to use something lint free like microfiber or like obsama1 said, a coffee filter and rubbing alcohol to clean off the thermal paste on it. Once it's clean, there should be a lever, pull that up and remove the cover, take out the CPU gently and again like obsama1 said, not at an angle, do it straight.
After you removed it, put in your new cpu, make sure the golder arrow lines up with the golden arrow on your motherboard and put it in, DO NOT PRESS it in if it doesn't seem to go in. If it is AMD make sure the pins go into the holes, it should "plop" in, if it's intel just give it a little wiggle and then put the cover on the cpu and fasten the lever. Apply the thermal paste, you should only be using a pea sized amount or a grain of rice. Once that is done put on the heatsink and voila, you have replaced your CPU.