Il Bruche's recipe will work fine for a dry with a champagne or wine yeast. I've never done a semisweet. Just a few things...
Heat your water to dissolve the honey more easily. Heat to at least 165F and hold there for ten minutes or so to pasteurize. It's not strictly necessary (our ancestors didn't bother) but giving your yeast an open playground to go wild on makes them happy, and happy yeast makes for happy drinkers. Boil and skim, or don't. I personally don't bother; again, they didn't back then and I feel that all those little impurities that are removed in the process add complexity (but potential off-flavors) if left in. If you're using good honey it probably won't matter.
Use good honey. Mead's dominant flavor should be honey without the sweetness, so taste your honey first and try to imagine it without the sugar. If you don't like it you probably won't like the mead it'll make.
Use good yeast and keep it happy. Yeast likes the correct temperature (shown on the packaging -- read those directions and follow them, your mead depends on it) and while it's usually pretty good at fighting off competing microorganisms, the less fighting that it has to do the happier it will be. Red Star Premier Cuvee was what I started on and is ridiculously tolerant of mishandling (it's actually recommended to restart stuck fermentations) but it's notorious for a rocket fuel aftertaste, particularly if you're generating high levels of alcohol; extended aging (~4-5 months at least) will be necessary to remove this. Lalvin's K1V-1116 and EC-1118 (I might be misremembering the strain names but I think I'm close) are almost as durable and are kinder on the flavor, and are also efficient producers of alcohol and carbon dioxide. I'm sure that there are other good ones but these are what I have the most experience with.
With these dry yeasts, follow the reactivation directions on the packaging at a bare minimum; even better, make a starter culture to really give them a running start. Aerate your must before or after pitching the yeast by vigorously shaking the fermenter, as yeast need plenty of O2 at the beginning of fermentation. Consider adding some yeast nutrient or at least a bit of grape juice or raisins; wine yeasts have evolved to live on grapes, and honey isn't an optimal food for them. If you don't your fermentation will still likely succeed but it will take longer. The most important thing here is to make conditions as optimal for the yeast as possible while making everything else uncomfortable, as the quicker the yeast colony is established the less chance that there is for something to go wrong; this is why some recipes include citrus or acid blends, as low pH's favor yeasts and inhibit other microorganisms. They are not strictly necessary but certainly don't do any harm and may improve the taste for some.
Do not under any circumstances add yeast to must that is over 100F or you will kill your yeast. It'll still ferment with the wild stuff but you may not like the result.
Add all of this into a sanitized container fitted with an airlock and place it in a warm, dark area with easily cleaned surfaces in case you have an overflow. In my experience mead never does this; honey is too poor a food for wine yeast for explosive fermentation but it doesn't hurt to be ready for one anyway. You should start seeing activity in a day or two. At that point leave it alone.
Live yeast, dead yeast, yeast byproducts, and other assorted odds and ends will settle in the bottom of the container. At best these will cloud your mead and at worst, will introduce off-flavors. Once a month or so rack the mead into a new sanitized container (fitted with an airlock of course) using a siphoning tube. Homebrew shops sell these with a convenient spacer on the bottom to keep it out of the lees and they're cheap.
After two or three months there'll be little or no activity at the airlock -- your yeast has pretty much consumed all the sugar. You'll also notice far less sediment at the bottom and probably clearer mead. At this point it's pretty much done fermenting but more aging is never a bad idea. Continue racking monthly for 4-6 months or so, or maybe even more. Be sure to taste it at each racking (if you start the siphon with your mouth like I do you won't have a choice) to see where you're at and figure out when you'd like to bottle. It should not taste sweet after a few months. If it does, your fermentation stuck and further action is required.
When you think that it's ready decide if it's clear enough for you. Further aging will help clear it; also, refrigerating the fermenter or leaving it outside overnight if your nights are cold will help force the now-weakened yeast into dormancy and will tend to throw most of the remaining sediment out of suspension, further clarifying it. Fining agents can shorten this process but are probably a needless complication for a first batch. This probably won't affect the flavor but it will make it look far nicer. At that point you can bottle or keg as you like. If you're bottling, seriously consider purchasing a bottling wand. They're inexpensive and extremely useful. You'll see what I mean the first time that you use one.
After that, wait. Mead doesn't age as well as wine but should continue improving for up to a year or possibly more. Sometimes even a month of aging can make a huge difference in taste.
Sweeter meads are actually more difficult. You must either use a yeast that can't handle all the sugar (and figuring this out is more art than science), or knock the yeast out chemically (sulfiting) and add more sugar or preferably honey, or use an artificial sweetener (which probably will have a negative effect on the flavor). The choice is yours but drys are the simplest.
Carbonation is simply a matter of sealing up the mead while the yeast is still active. Sealing earlier in the process will produce more carbonation, as will bottling with a small amount of sugar if the fermentation is already complete. Corked wine bottles will not work for this. Mead naturally will have a small amount of carbonation; stirring before bottling and extended aging will remove this if a still mead is desired.
