I am beginning to build my first system, but I neglected to think of the thermal paste. I had seen where stock coolers already had the paste on the stock coolers but I am unsure of whether or not an i5-3570k's stock cooler has it already applied. Also, my motherboard is the ASRock Extreme6 with the CPU cover for protection; so do I just install the CPU, close the cover, and put the area of the thermal paste on the cooler onto the cover? Thanks!
Don't use paste with stock coolers. Or any cooler. Since you have such a beefy CPU, buy a Hyper 212+ or a cooler like that, and buy a tube worth of either Arctic Silver 5 or MX-4, good stuff. And no, thats not a CPU cover for protection - all modern Intel sockets have that because it hold the CPU down, connecting the pads of the processor to the pins of the board - it's needed to secure the processor. And yes, all you have to remove the lid on the cover, open the cover, put the CPU down, place the cover over it, secure it, and then put a REALLY thin, short, vertical line of paste on the processor over the die - this will ensure the best cooling operation.
Sorry, for some reason, I had it set in my mind that there was a plastic covering over the IHS. I can only use the stock cooler at the moment, but I will get a 212 later i.e. no overclocking right at the moment. The stock cooler has three grey stripes that I assume are paste marks.
Yes - clean it off, pure garbage, it'll cool better if you use an aftermarket one.
How to clean off - paper towel with alcohol, wipe it 100% off until there's no residue wiping onto the paper, the wipe it down with a microfiber cloth to get the lint off and to give it a nice shine - cleaner it is, better it cools. Then just sit it down on the CPU & you're good to go!
And also, DON'T SPREAD THE PASTE. IT'S A DUMB THING TO DO.