Instant coffee is a nice thing if you don't have anything else that tastes more like coffee...but that really is the last resort, because it is a substitute and it tastes like it.
Chewing coffee grounds is not recommended by the ADA. But it will work if you give it enough time. Downside is people won't stop telling you that you have something in your teeth for the rest of the day . That, and it's generally an unpleasant experience.
That leaves camping coffee makers, percolators and french presses.
Outdoor / Non-Electric Coffee Makers
Like my friends who were in the boy scouts always told me, it's good to be prepared. Coleman is pretty much the leader in mainstream camping cooking equipment and they have come up with some brilliant solutions for this acknowledged human necessity that is coffee. Coleman Camping Coffee Maker has got to be my favorite. It was designed for a coleman gas grill, but could be used over an open fire as well.
Percolators
Percolators, boil the water and the coffee sits in a basket inside. After a period of time, you will see the top show a darker and darker color as the coffee is brewed...pour and enjoy!
Espresso Percolators
Just a tiny pressure percolator you can sit over an open flame but it really makes a strong cup of coffee. The pressure extracts every bit of caffeine out of the grind and it is evident. As usual, espresso really packs a punch and one shot can give you a good boost when you need it quick.
French Press
Basically, the French Press is about as simple as you can get. You boil the coffee in a separate container, and pour it into the press, wait, then press the grounds to the bottom and pour for a delicous hot cup of coffee. It keeps the grounds out for the most part, but the glass ones are difficult to camp with. The best part of this solution is you don't risk burning it.
Bodum 1548-01US Brazil 8-Cup (34-Ounce) Coffee PressCoffee Presses)
All in all, it's not a difficult task, a lot of people boil coffee and then let the grounds settle. Turkish style.
Desperation can lead down many paths, as long as it ends with coffee, you're okay.
Have a cup!