Stop whatever you're doing right now, put off your comp. Get any thermal paste. Don't bother about Arctic Silver right now.
Scrape off any thermal sticker residue with a blunt instrument. Careful not to break anything.
Use a good quality solvent to clean heat sink contact area and CPU surface. Clean thoroughly until everything shines like in the Pril ad

Any solvent with minimum additives will do for now. Preferably flick your girlfriends acetone based nail polish remover.
Now apply a very small amount of thermal paste on the cpu core to fully cover the top surface. Quantity is critical. Excess will only reduce thermal conductivity and worsen matters in a few months when it starts caking.
Use a pea drop of paste, and a credit card sized stiff cardboard to spread paste evenly, in one direction, straight strokes until fully covered. Patience is the key here if you wanna get max coverage with min paste.
It's not necessary to apply paste on heat sink. Just give it a small left right twist once seated on CPU to spread paste. Clip on the retainer.
That's it, and don't forget to replace that nail polish remover before you get caught for stealing.
Cheers,
Keith