I've been making coffee this way for about a decade now, so I can definitely offer a good process. First of all, it is essential that you use coffee that is ground for use in a French Press pot. It is a coarser grind than for other methods of making coffee. I grind my own beans to get the right grind. I assume the coffee you have on hand was ground for French Press. If it is too fine, it will clog up the pot and you won't be able to "press" it.
I don't know what size of pot you have, but I use a heaping coffee measure for each cup of water. Put the ground coffee in the pot, bring water to a boil in a separate kettle/pan, then pour in just enough water to wet the coffee grounds. Stir the gorunds to moisten all of them and let sit for one minute. Pour in more water, to come within about 1/2 inch of the top of the French Press pot. Stir again, put the plunger part on top, and let sit for at least 4 minutes (I let mine sit/steep for 6 to 8 minutes - the longer, the stronger the coffee). Very slowly and carefully, push down on the plunger until it gets to the bottom of the pot. Don't force it or you can end up with scalding hot coffee on your hands.
This should make a really good cup of coffee.