To answer your question about what you need to do when replacing your CPU cooler. (This is what I do)
The best way to do this is to first remove the motherboard from the motherboard tray/case. Depending on the 3rd party heatsink you get, you will most likely need to do this to install the back plate that would be included to anchor the heatsink.
Once you removed the motherboard, remove the Intel/AMD heatsink. Use a q-tip, lightly dipped in isoprophyl alcohol. You will use this to rub the old thermal paste off the CPU. You can either remove the CPU to do this, or if you have steady hands, do this with the CPU installed the motherboard (recommend you remove the CPU, especially if you have the original case it came in to "rest" it on). Remove as much, if not all, the old paste away and give it a chance to air dry off (will be fast).
Once you cleaned the CPU off, you can reinstall the CPU into the motherboard. Next, add new thermal paste onto the CPU. The way I spread it on is to use a ziploc bag, hand inside, and carefullly spread it on. You don't need a lot of paste on it, just a good layer covering up the exposed metal. Once on, you install the new 3rd party heatsink, following its instructions as needed (depending on the model, you may or may not have to install a back plate)
