I covered heating the water in my previous entry, now I'll go over what I do with the hot water.
Espresso is my favorite coffee preparation method, but pour over is a close second, so that is what I go with when camping. French press, cowboy coffee, even moka pots work as well, but I like the balance of flavor and simplicity that a pour over device offers.
Dripper: I use a plastic Melitta cone with Melitta filters when camping. I like the light weight and the cost. If it breaks, no big deal. Another plus is that your pour over technique doesn't have to be perfect with one of these.
Grinder: The Hario Mini Mill is perfect. The plastic is surprisingly rugged and the grind quality that you get for your money is fantastic.
Water: The water is often my favorite thing about backcountry coffee making. In my opinion, water from the high Sierra is some of the best tasting water on earth, and it makes for great coffee. If you've never tasted it, I'm sorry, because it is delicious.
Cup: I usually use a small round tupperware container. It's super light and it works. Not much else to say about it.
Beans: Anything fresh.
Now for what I use depending on the activity*:
Car camping/leisurely backpacking with friends (0-10 miles per day): I bring everything listed in this blog and the previous entry. For trips like this, weight and size are not concerns so I can go all out if I feel like it.
Moderate solo backpacking (10-25 miles per day): I'll bring the kettle, stove, and the cup. Now I'm not proud of this, but I tend to use Starbucks Via on trips like this. It is lightweight and more convenient than doing pour over in the morning. Yes, the coffee is crap but it is the best instant that I've ever used.
High mileage backpacking (>25 miles per day): No coffee. I tend to do no-cook breakfasts on trips like this in order to maximize time available for hiking and to minimize fuel weight. I make up for the lack of caffeine by eating snacks that contain caffeine.
*I should mention that I can be a bit of an ultralight backpacker depending on the trip.