Brewing Mead is similar to brewing the Sugar Wine described on the Getting Started page, only in place of commercially prepared sugar you use honey. You need to use about 3lbs of honey with water bulked up to a gallon. To prepare the honey, boil it with water, allow it to cool, and skim off the floating wax.
Dissolve the prepared honey water in to cold water, add a teaspoon or two of yeast, baker's yeast will do, mix it all up, pour it in to a clean fermentation vessel, and seal it with a bung fitted with a water-filled air lock.
The yeast will digest the dissolved honey and release two by-products: alcohol and carbon dioxide gas. The carbon dioxide gas produced during fermentation will be safely vented through the air lock.
When the yeast has consumed all of the dissolved honey the fermentation process is over. This will be indicated when bubbling through the air lock ceases. The resulting brew will then be cloudy, and there will be a sediment of dead yeast cells at the bottom of the fermentation vessel.
To remove the cloudiness, if it doesn't precipitate as more sediment, you need to add finings, such as isinglass, or a little brewed strong tea, or a little citric acid from oranges, lemons and the like. Such inclusions will cause suspended particles in the brew to precipitate down and form yet more sediment. When the brew is clear, siphon it off in to another vessel for subsequent bottling, with the siphon tube positioned above the sediment so that the sediment is left behind in the fermentation vessel.
For more information, check out the Wikipedia article about mead at http://en.wikipedia.org/wiki/Mead