My first batch of beer was a malt extract pale ale kit. Turned out excellent and I've been hooked on homebrewing ever since. Simple brews like pale ales are the ones that will turn out the fastest.
The brew process takes about four hours from start to finish including prep, sanitizing, boiling the wort, transfer to a fermentor and pitching the yeast. The pale ale kit needed four days in primary fermentation, then you transfer to a secondary fermentor and let it sit 7-10 days. Then you bottle and it'll sit in bottles for a couple of weeks while it builds carbonation. With the pale, we were drinking initial beers three weeks after the brew and it got progressively better the longer it was in the bottle.
But the higher the gravity of the beer, the longer the fermentation process will take. I got a Grand Cru sitting in my closet that I had in primary a month and is about three weeks into secondary fermentation. Even after we bottle it will be a couple of months before we can enjoy that one. A barley wine style ale can sit in fermentation for over a year.
For anyone that wants to brew their own, I would suggest getting a good equipment kit (about $100-$150) right off the bat with glass fermentors instead of dealing with plastic. Although it isn't expensive, its cool to go in with a friend on the startup costs and it helps to have a second person assisting with the brewing. You can also get less expensive kits for about $50. As a beginner, it is easier to get a malt extract kit. They'll start at about $20 and up and will make a five gallon batch although you will lose some of that during the transfers. Ales are the easiest because they ferment at 65F to 75F so you can just put them in a closet. Lagers will require refrigeration during the lagering process and will have to be in the 30s.
The next levels of brewing are partial mash and full grain. More complex as you move up but the materials will cost less and a lot of people will argue that it produces better brew. It also requires additional equipment so the initial startup cost jumps up.
At the height of brewing madness, I was brewing a batch a week but I was running out of bottles and storage all the time. It's also fun to name your brews. We've normally named our brews for specific events that occurered during the brewing process. I've brew several different styles but my favorites where the Imperial Stout (the Imperial Grackle), a Wildcatter Stout clone (Chicken Wing Stout), a Hefe-Weizen (Heavy Weight Hefe for the thermometer we broke in the brew kettle), a trappist ale (the Drunken Monk since we were so hammered when we finished brewing it that we forgot to add a pound and a half of corn sugar to the brew and wound up jamming it into the fermenter), an IPA and an Octoberfest called Ratoberfest (don't ask).
I recommend homebrewing to anyone who loves beer or wants an interesting hobby. There are worse ways to kill an afternoon than brewing up a batch in the backyard, barbecuing, drinking beer with your buds and maybe even some cigar smoking.