Water: Without water, there would be no beer. Water is the main ingredient in beer, and therefore must be treated with respect. The minerals in water have a great effect on how the beer turns out.
Fun fact: This is the reason why you see specific regions being known for a particular beer. The water in the area contains minerals that lend themselves to making one style of beer particularly well.
Malt: Malt is used to provide the sweetness for the beer. It is also used as the food for yeast. Traditionally, Malt means Malted Barley or sometimes Wheat, but today, it can be generalized to include most grains.
Hops: Hops are used to provide bitterness to beer, balancing out the sweet of the malt. The hop plant is a fast growing vine that produces soft green pine cone-like flowers. These are what are used in brewing. Hops are often used in pelletized form, especially for home brewers.
Yeast: Yeast may be the most important ingredient. Yeast consumes the malt, and in the process creates ever-important ethanol and carbon dioxide. The use of a different yeast can drastically change the resulting beer. Some yeast is used because it leaves very little flavor and give a particular finish, allowing the hops and malt to shine, which is common with many varieties of lager. Others, such as German Hefeweizen yeasts, are used because they give the beer particular flavors that without the yeast, would be difficult to include. There are numerous books solely on yeast. Read up it you are interested.
Things you may see that describe beer:
Ale: Beer that has been fermented using an Ale Yeast. Ale Yeasts generally ferment around 68 F.
Lager: Beer that has been fermented using a Lager Yeast. Lager Yeasts generally ferment around 50 F.
ABV(Alcohol By Volume): Pretty self explanatory. The percentage of alcohol in the beer, calculated by using the volume of alcohol versus the total volume of beer. Typically between 2-12%
SRM (Standard Research Method) Ratings: This has to do with the color of the beer. The SRM Numbers are generally as follows:
20-40: Copper/Very Dark Amber
40 and above: Black
Don't over think this one, it only deals with the color.
IBUs (International Bittering Units): This, obviously is a measure of how bitter the beer is. The higher the IBUs, generally the more hop character and the more bitter the beer will be. Some bars will display the IBUs, which is very helpful in choosing a beer based on your hop-taste. The scale is generally as follows.
0-20 IBU: Little to No Hop Flavor
20-45 IBU: Noticeable to Pronounced Hops
45 and above IBU: Really, Really Hoppy
Now, IBU alone isn't enough to really tell you if a beer is too hoppy. I have had a 82 IBU beer that i find to be very balanced. IBUs are meant to tell you how much hop character the beer has.
I will keep updating as I go. If you think I should add something, email me!