Lets begin with water. Water is the major component of your beer volumetrically, and historically it was one of the key variables that differentiated breweries. Prior to activated charcoal filters and reverse osmosis the water available to a brewery was limited to the local supply. As you should know, the concentration of various ions in water can vary greatly from locale to locale. The major ions we worry about in brewing are Na, Cl, Ca, HCO3, SO4, and H2S (this is a nasty one to have in your water).
Luckily modern technology affords you several options as a brewer. First get a copy of the water analysis from the local water district. Here in Seattle the water pretty much just kicks ass as is. I happen to be a bit anal so I run it through an activated charcoal filter to remove organics, lead, mercury, and chlorine. Although, you could probably use Seattle tap without any problems. If you want to go world class you can buy a reverse osmosis sytem, at which point you have essentially deionized water that you can add ions back in at the concentrations you want. Most water modifications are done to get your water to match the water historically available at a brewery who defined the style you wish to brew. The other way to get good water is to go with bottled water. Now, I'm not recommending Perrier, but more along the lines of 1 gallon jugs of Safeway water.
The last aspect I'll touch on with water is pH. Typically you want you're beer at an acidic pH (below 7) in the range of 5.8 - 5.2 for the mashing process (more on mashing later). When the grain is added to the mash the pH is lowered to approximately the correct range. In cases where you use roasted barley, the some buffering with carbonate can be very helpful. Refer to any of numerous sources on basic brewing chemistry (Designing Great Beers by Ray Daniels does an okay job) for more details.
Hops are a critical component to beer. Typically whole books are written on hops and I'd suggest you refer to the references I've previously mentioned for a more complete discussion. Perhaps in the future I'll write more on hops. Essentially, hops are a flower cone with excellent bittering properties used in beer to offset the sweet taste of malt. The vast majority of hops grown in the United States are grown in the Yakima Valley of Washington State. The bittering properties of hops are due to a compound called alpha acids. When purchasing hops you'll note that a value in terms of %AA is given. This tells you the percentage of alpha acids in that particular lot of hops. Now alpha-acids in the hops are highly insoluble in beer unless they are heated to isomerize (cis-trans isomerization). This is the reason we boil hops for a minimum of 60 minutes to add bitterness to our beer.
In addition to bitterness, hops are used for flavor and aroma. However, the chemicals that add this characteristic aren't alpha-acids. Flavor and aroma chemicals are highly volatile and are easily driven off if boiled to long. For this reason we make late hop additions. Hops added 10-15 minutes before the end of boiling are typically called flavor hops, and hops added in the last 5 minutes are called aroma hops. For some styles that the hop-heads love (eg: IPA's) brewers will add hop leaves to the cooled fermenting beer. This process is called dry hopping.
Last but not least, we'll talk yeast. Yeast are the single most important part of your beer. Without yeast you have just sweet wort (wort, pronounced like wart, is the sweet liquid before it's been fermented to beer). An interesting experiment is to make one batch of wort, divide it in half, and pitch (brewer's word for inoculating) different yeast in each portion of wort. Luckily for brewers today companies like Wyeast and White Labs provide homebrewers with extremely high quality liquid yeast cultures. There are a plethora of yeast strains available and I suggest you consult the online literature from the manufacturers for more information on the caveats of each strain. A note on pitching rates. Homebrewers are known for chronically underpitching their worts. If you don't add enough yeast you are giving contaminants such as bacteria and wild yeast an excellent chance to get growing in your wort and ruin your beer. The best way to fix this is to grow a yeast starter. In a sanitized mason jar (boiled or sanitized in chlorine water) add a solution of corn sugar or malt extract in water (3/4 cup in a pint and a half of water). Add your yeast to this solution after starting it according to the manufacturer's instructions. Seal it up with a stopper and airlock, and let it sit for a day before you're ready to pitch. Ideally you start this a day or two before you plan to brew. Never ever ever leave cooled wort out without pitching it, you're just asking for contamination in your beer.
Well thats all for today. Tomorrow I'll walk you through your first extract brew. After that we'll try the whole she-bang with an all grain brewing example. Till then have a good one.