Applying thermal paste to new CPUs is a daunting task if you've never done it before. It's a piece of cake if you have.
The first thing to do (after you've gotten yourself your new CPU, motherboard, and thermal paste) is to go out and get yourself some microfiber wipes.
If the processor is already installed, remove the fan and processor and, using the microfiber wipes and 91% isopropyl alcohol, clean off ALL the old paste from both the fan's heat sink and the processor chip. Depending on how long the processor has been in use, this could take quite a while but it WILL eventually come off.
If it is a new processor, you may still have to clean manufacturer-applied paste from the cooling fan the same as you would from an old processor installation, but this will be much easier. Just use the microfiber wipes and some 91% isopropyl alcohol and VERY carefully clean the top surface of the CPU. Be especially careful not to touch the top of the CPU contacts on the bottom of the processor.
Now you "stain" the CPU. Again taking special care not to touch the contacts, apply a small amount of the thermal paste (I recommend Arctic Silver -- it's easy and its applicator tip is JUST right) to the top of the CPU, use a credit card or something similar to spread it thinly over the entire top surface, and then wipe it off carefully ("carefully" is the governing philosophy throughout this entire procedure) with a microfiber wipe WITHOUT any alcohol. This fills any irregularities in the CPU surface with thermal paste and it will run cooler for life.
Now, install the stained CPU in the socket and clamp it down.
Next, apply the thermal paste to the CPU. For most Intel chips, this is done by applying the paste in a thin vertical line centered on the CPU cap and running about 3/4ths or so of the total CPU height. For most AMD chips it is applied as a dot in the center of the chip about the size of a very small pea or a large match tip.
Now, carefully install the cooling fan. The installation of the fan's heat sink should spread around the cooling paste correctly. You don't need to spread the paste at all -- installation of the heat sink does all the work..
A little excess won't hurt. A LOT of excess could. Thermal paste doesn't dry hard for a very long time, if ever. Indeed, if it does dry hard, it's time to think about cleaning and reinstalling the thermal paste.
Also, keeping your computer clean inside will make it run cooler. They get gummed up with all this dust remarkably quickly, and can be cleaned out pretty well with those little cans of air. Do it outside, though -- they collect GOBS of dust even when you keep your home or office immaculate.
Two excellent freeware applications allow you to check and/or continuously monitor your CPU temperatures and other aspects of your system's ongoing operations. One, which is just a nice clean monitoring application, is the open source Open Hardware Monitor, available at http://openhardwaremonitor.org/ . Another, which enables you to do stress testing and diagnostics in a wide variety of ways, is OCCT ("OverClock Checking Tool"), a French application that lets you load your CPU, RAM and GPU to 100% capacity with various data sets and graphically monitor their temperatures under load. It is available at http://www.ocbase.com/ .
I hope this helps. I followed these procedures building my Core i7 machine and the CPU runs normally at an exceptionally cool 34 degrees C in normal usage. Even blasting it continuously for hours at 100% on all four CPUs, and all of its 16GB of RAM I can only get the maximum temperature of any of the four cores up to 54 degrees at peak at the 3.8 GHz burst speed. I could probably overclock it over 5 GHz without having it even start to breathe hard but the speed is adequate for now and I am looking for reliability rather than dominance.