Melting snow for drinking water is a simple task, but since it is so fundamental, and fuel is so precious in the mountains, it is worthwhile analyzing. The basic procedure is idiot-proof: put snow in a pot, put the pot on a stove, and wait. Below, we go over some options. It seems there are a lot of theories on the most efficient practice, but little evidence.
Mountaineering: Freedom of the Hills (available in our library) doesn't have much to say other than to be careful to get snow from a clean source (not near the pee spot), to collect it in large chunks rather than powder (to make the process "simpler and neater"), and to always start with a bit of water in the pot, otherwise the pot can burn. If cooking in a tent, bring in a bunch of fresh snow before going to bed so that you don't need to leave the tent later. Melt snow the day before for the next day's supply, since otherwise you may delay the group's start the next day. If you have enough fuel, make hot water and sleep with the hot water bottles as a nice bonus.
If you look at some threads on supertopo, they suggest continuously pushing the snow down, since as water appears in the bottom, it sucks up into the snow, leaving a dead space, and thus the pot can burn.
Jon "Lofty" Wiseman, author of a survival guidebook, writes
Melt ice rather than snow---it produces a greater volume faster for less heat: twice as much for half the heat. If forced to heat snow, place a little in the pot and melt that first, gradually adding more to it. If you put a lot of snow into the pot, the lower level will melt and then be soaked up into the absorbent snow above it, leaving a hollow beneath which will make the pot burn. Lower layers of snow are more granular than that on the surface and will yield more water.
Colin Haley has an excellent article on cascade climbers from; it covers more than just cooking, but we just quote the cooking section here. He also covers stoves and fuel, which we do not discuss on this page.
The best cooking pots are always made of aluminum. Steel pots are far too heavy, and titanium does not conduct heat well (and is only marginally lighter than aluminum). If not using a Jetboil-type stove-pot-combo, use the lightest aluminum pot you can find around 1.5 to 2.0 L capacity. Unfortunately, due to concerns of Alzheimer's Disease, most modern aluminum cooking pots are made with a coating that adds substantial weight. The best place to find good cooking pots is often Goodwill or other thrift-stores, where you can still find old, cheapo, aluminum camping pots.
Elsewhere, along similar lines of reasoning, Haley has made the point that for a 1 day trip, titanium pots might be better than aluminum since they are slightly lighter. For longer trips, since titanium heats up more slowly, it cost more fuel, and therefore aluminum is the better choice.
Is this reasoning valid? There are other factors, such as the insulation properties of the pot. Also, is it worth the weight to make an insulating jacket for the pot (jetboil style)?