1) Isopropyl alcohol is best to use if you have it. Just put some on either some tough bounty or on a wash cloth and slowly and gently rub it in. Do it this way so it doesn't spill all over your board. You can use nail polish remover too, shouldn't harm anything but just not as "pure" because they add stuff to it like gelatin and other things. I'd stay away from it personally or at least use a damp paper towel afterwards to clean up residue.
2) Cover the GPU (silve area) only with your thermal paste. It is made to take heat from the gpu to the heatsink, so putting it everywhere else isn't what you should do.
3) Use the spread method, it will ensure you get it everywhere. I'd start with the "pea method" and then use a piece of index card to spread it all around in a thin layer. The layer should be thin like a piece of paper or so.
You should only use ispropyl alcohol of 90% or more. It is a pure substance that will evaporate without leaving anything behind, and it costs less than a dollar. Don't use so much alcohol that it runs all over your board. Don't use nail polish remover as it will leave behind all the extra ingredients, like perfume. Also don't touch the GPU with your fingers, even if you wash your hands first, you will leave behind oils.
I use Arctic Cooling MX-4 and apply it with small applicator brush (ironically, like a nail polish brush) that I clean with alcohol and dry first. Cover the entire GPU surface (the silver part). Just think that the ideal situation would be metal on metal, but due to imperfections in the GPU surface, the thermal paste is needed to fill in those micro-dips and valleys. So use a very, very thin layer, to the point where you can almost still see the lettering on the GPU. Clean off anything that goes over the edge or onto the board, a Q-tip works well for that.
I'm using MX-3, which has the same thermal/conductivity characteristics as MX-4, but MX-4 is thinner and easier to spread. I have been seeing reviews of heatsinks where the reviewer says that MX-4 is all they use. Good stuff!
By the way, I am totally a fan of using something like a small brush (like a nail polish brush) to apply the paste. I have never had much luck with spreading it with a credit card or my fingers (wrapped in a plastic sandwich bag). The brush is very fine and accurate. I'm actually using the brush applicator from a Zalman STG-1 thermal paste container. I definitely don't like the single drop in the middle technique, either. It never seems to cover the entire surface.