1) Remove the stock cooler that you mounted
2) Remove the thermal paste that is left on the CPU with at least 60% rubbing alcohol and a clean cloth
3) Read the H60 installation instructions. If you are not sure which socket type you have or which bracket to use post your CPU model here and we will help you
4) Make sure the CPU is clean of all debris and install the H60 bracket according to the installation instructions, there is no need for any extra thermal paste because the H60 has thermal paste already applied to it.
Ah from the stock fan. Well clean it off using something like a cotton bud and some sort of white spirit or whatever. It's not too hard to get it off https://www.youtube.com/watch?v=x9MJUuU58vE Just make sure not to get any liquid on the motherboard itself.
Once it's cleaned up you can look to mount the H60
I use a plastic spoon to get any larger bits (GENTLY) and a cotton swab (aka qtip) with a tiny bit of rubbing alcohol to take off the residue. Works like a charm, and th excess rubbing alcohol just evaporates.
No stores are open right now, so I'm gonna use a 93% alcohol with cotton bud. And I think I'm gonna remove the CPU from the motherboard when cleaning it, just to be safer.
Edit:
Oh I can't. Well, I'm just gonna clean it while it's on the motherboard. Super nervous about this.
Edit 2:
I think this must be good enough, can't seem to get it any more cleaner.