What is Lautering?
Once your mash passes an iodine starch test, you are ready to "mash-out" and lauter the grain. Lautering is simply a method to assure that as much sugar as can be, is removed from the grist. The basic method is to bring the mash up to 77°C (170°F), to stop enzymatic activity, then "pour off" the wort into the boiling kettle while filtering the spent grain from it. "Pour off" is a bit of a misnomer, since in the ideal situation the grain will be used to act as a filter by building a grain bed which will catch additional bits of spent hulls and grain particles, and also in such an ideal situation a process called sparging will also be used.
The Simple Lauter
The section is a description of a "bare-bones" lauter, and is not the recommended process. However, this process will produce acceptable wort, and could be used by a first time all grain brewer. First, bring the mash to 77°C (170°F) applying heat. This can be accomplished by adding measured amounts of water, but this additional water will need to be figured into the overall water volume, and too much water will require a longer boil, and it gets kinda sticky from there. If you can't apply heat directly to your lauter tun, move the entire mash to a kettle that you can heat. Be sure to constantly stir the mash while applying heat to avoid burning the particles (both spent grains and the dissolved sugars).
Now, pour (and this time I really do mean pour) the entire mash through an oversized strainer and into your boil kettle, or an intermediate container, if it's currently in the boil kettle. Of course, if you are pouring into an intermediate, you can filter the wort again while pouring back into the boil. The goal of this is to remove all particles of spent grains, because once you begin the boil, hulls will stew undesirable flavors into the wort. Once the wort is free of debris, you're done.
The Professional Hobbyist Lauter
This method is the preferred one, and is the one used by this. If you cannot apply heat to your mash tun, move the entire mash to a kettle. Bring the mash to 77°C (170°F), stirring to avoid burning. Your lauter tun should have a false bottom, and a spigot. You will want to use "foundation water" in your lauter tun; water at 77°C (170°F) should be put in the tun to fill it a few inches above the false bottom. This is to gently lay the spent grains on the false bottom to improve the likelihood of a good grain bed to form and also to avoid stuck run-off. A stuck run-off is a situation where the spent grains have compacted under their own weight so as to prevent wort from passing through the grain bed.
Now scoop some of the mash out of the kettle and lay it in the lauter tun. Then add a bit of sparge water to maintain the level of liquid above the surface of the grains. Sparge water is simply fresh water at 77°C (170°F). By keeping the surface of the liquid above the grain, the brew master keeps the grain bed from collapsing while avoiding too much liquid which would cause the grains to float too much. The brewmaster (you) will keep alternating in adding sparge water and adding mash, until all of the mash is in the lauter tun. Then the liquid can be drained.
While slowly draining the wort into the brew kettle, sparge water is sprinkled into the top of the tun to maintain the surface of the liquid above the grain bed. This is what is affectionately called sparging, and is done carefully so to not disturb the grain bed. Up to 19L (5 gal) or sparge water will be used, including that used for foundation water and building the grainbed. However, some of this water will be lost to the lauter in keeping the surface levels correct until the end. A brew master must calculate the required amount of water considering the overall use in the entire brew process, but a general guideline to follow is (kg grain) x 4.2 = liters or (lbs grain)/2 = gallons total sparge water.