Backpackers have similar concerns about lightweight, portable stoves. You have three basic options - gas cartridge stoves (Pocket Rocket or similar), alcohol stoves, or solid fuel stoves (Esbit). What works best (is the most efficient for the weight carried) depends upon the length of trip.

Alcohol is the lightest for trips of less than four days, more or less. Stoves are very light, as little as an ounce or less, and are frequently made from soda popcans. There are also many commercial stoves available - the classic alcohol stove is the Trangia, weighing all of three ounces! These stoves will take any of the various varieties of alcohol, so it is not difficult to find something that will boil your water. Alcohol is not as energy dense as isobutane, one of the more popular of the gas cartridge varieties.

Gas cartridges have a threaded valve onto which is screwed a burner head. Operation is simple - screw on the stove, open the valve, light, and start cooking. You do have the dead weight of the cartridge to drag around, so this rig becomes lightest only on longer trips, more than four days or so. The cartridges can be hard to find in small towns. Operation is almost as simple as using your kitchen stove.

Solid fuel "stoves" can be the very lightest - something like the Titanium Tri Wing stove features by Hikin' Jim as stove of the week holds the Esbit brick which is lit and you get to cooking, although realistically you are pretty much limited to boiling water. You can improvise a stove from tinfoil if necessary. Esbit is not necessarily found in small towns.

With all of these, efficiency is increased by proper use of a windscreen and suitable cooking pots. You want a lid on whatever pot is boiling water to avoid squandering fuel. Carry a few sheets of aluminum foil for making a windscreen.

The short answer to your question is a Trangia Mini 28 cookset, a quart of alcohol from the hardware store, and a pop bottle used as a fuel container (suitably marked), plus windscreen. If you wish, you can augment this with a Pocket Rocket from MSR and a few isobutane cartridges. It works well with the Trangia cookset, which is adequate for one or two people.

These systems work well, down to about freezing, more or less. In colder conditions, you want to go to any of several liquid gas stoves, which are heavier but put out the necessary heat that allows you to melt snow.

Don't forget the campfire, for which you only need carry a match. It is the lightest of all, but is not suitable for all conditions. It will warm you as well as your food, and it serves as an admirable signaling device, if you wish to be found.