I think all of us forgot: You'll have to put on thermal paste between the cooler and the CPU. This is very important, if you didn't know. If you ignore it, the temps will rise very high (which is bad).
There will be some thermal paste when you remove the cooler, which is probably dried out. You should use isopropyl/isopropanol rubbing alcohol 70-90% on paper towels to remove it. Some advice against paper towels, but if you use rubbing alcohol on them it's completely fine.
To apply the paste itself, i would recommend the "pea method" which i used myself without any struggle the first time i built a computer. Follow this guide and you should be good:
http://www.tomshardware.com/reviews/thermal-paste-heat-sink-heat-spreader,3600-5.html...