I've experimented with various methods and I've found they all give similar results.
Keep in mind I tend to like real strong coffee. I just use the espresso grind my grinder is set too. A courser grind would probably be more typical, but I've made Turkish coffee before, which is an extremely fine grind, and Turkish is made similarily to cowboy coffee, so I use an espresso grind, which is somewhere in between.
I boil the water, and once boiling, I remove the pot from the stove, add my coffee (I don't measure, you'll have to experiment to see how strong you like it), and stir it a bit. I then set the pot on the stove till it boils again, which should not take long. I usually just let it boil a few seconds more and remove it from the heat. Then I just let the pot sit for a few minutes to let the grounds settle.
You then want to pour it slowly into your cup. You should not really get many grounds in the cup, most should have remained in the pot. Just make sure than you don't "drink to the last drop" and you will be fine. I find it best to brew a bit more than I will drink, so the grounds stay at the bottom.
This page shows essentially how I do it: