as Darkbreeze said, screw them all in a couple of turns, then go in an X-pattern a couple of turns each time to make sure you're getting even pressure on all the screws.
You might need a few tries to get it done correctly, but remember that
a) you have a lot of leftover thermal paste and
b) you have every reason to get it done right.
I nearly fried my rig once while replacing my stock cooler in a rush, so it pays to be very, very careful when you're doing these things.
1) Take your time and get it right.
2) Don't get frustrated if you can't get everything in the first time.
3) Re-check the instructions, make sure everything is correctly aligned, then try securing the cooler again.
4) If you do get frustrated, take a few minutes to just breathe. Go make a coffee or something, then come back to it when you're nice and calm again.