Yes, a thin layer is all you need on both the core and the heatsink.
It depends on what your CPU looks like. Check out www.arcticsilver.com
for good instructions on thermal paste application, it mainly pretains to their Arctic silver series of course, but still gives you an idea.... Also generally you just put it on the CPU.....if you've got a heatspreader on the CPU, I've heard the best method is to take a little thermal paste and with a rubber or plastic glove to rub the paste in the area where the CPU will make contact with HS and so that the grease gets in the microscopic valleys of the HS, but then to wipe off the top layer. Then you simply need to put about the size of a BB in the middle of the heatspreader and put on the HS, this will squish the thermal paste where it needs to be, because after all the CPU Core is in the middle of the heatspreader so it's not essential to put it over the entire spreader.
If it's just a CPU core exposed then simply put a little on the corner and smear it nice and thin across then entire core. Don't bother with putting any on the HS as trying to line up both 'piles' will just cause more troubles than if you simply smeared it out over the core.
Like I said though, if your chip has the heatspreader, I'd spread a little on the HS and then lightly wipe it off ( again, this is to simply fill the microscopic valleys not actually put thermal paste on the HS ), and after you've done that put the little dot in the middle of the heatspreader...once you put the HS on give it a little one degree twist in each direction to make sure all bubbles are squished.