Not to wax too philosophical, but brewing can really help people
achieve what psychologists call "Flow" experience. It's the way you
feel when you're in a situation that's challenging enough without being
discouraging. Some people see brewing as "meditation" and there's part
of that for some people. Also, there's a huge social part.

Perhaps the most obvious social part is that it's quite easy to make
friends when you offer them free beer. If someone's friends like bland
beer from macrobreweries, it's still possible to help them appreciate
beer for the way it tastes. The best way to do that is to brew beer
with that goal in mind. Sure, it's a challenge. It might take a few
trials and any given batch might not be that well-appreciated by
everyone. But little by little, it's possible to make people understand
that binge-drinking on Rolling Rock isn't that enjoyable when you can
get tasty beer on the cheap.

Another social aspect is that brewers tend to do things together.
Adults of any age or "walk of life" may belong to the same brewclub
and, usually, there's a very strong sense of friendship among brewers.
I know brewers and brewing groups in a couple of places and could help
people make contacts. Even if it's just sampling each other's brews or
discussing the amount of diacetyl that's acceptable in an Extra Special
Bitter, it can be quite fun.

Now, to get someone started on brewing. Many people start with cans of extract and it's certainly a solution. A cooler method is to use "ingredient kits" (e.g. from Grape and Granary) which include malt extract, grains, hops, and fresh yeast. You steep the grains and boil that solution with the extract. It's easy enough to do and it givessome amount of control. It's not the cheapest way but it works well. The
equipment one needs for these types of brewing techniques would mainly include a large kettle, a plastic bucket, a glass carboy, and some tubing. Homebrew supply shops usually sell equipment kits like that but it's easy to get many parts through other ways…

Among homebrewers, "all-grain brewing" is often considered the advanced step. It's not that much more complex and it's usually cheaper to do (especially with bulk grain). It does require a bit more equipment and more time on brewday. The equipment needed can be as simple as two plastic buckets. One has small holes drilled in it and serves as a false-bottom while the other one has a spigot. Some very good brewers
use that kind of a system and it works quite well. What I use is the same thing except that the bottom bucket has a heater element in it so I can control temperature. Other people use an Igloo-type cooler with a manifold in it built with some copper tubing in which slits have been cut. Other people go nuts and have a semi-automatic system made of stainless or even copper with all sorts of pumps and heat exchangers.
All of these achieve the same results: quality beer.
The basic principle remains the same. If you want to brew…
You need to mash grain at a certain temperature (150F to 158F, depending on what you want to achieve) for a certain amount of time (20 minutes to an hour or so). You then need to pour hot water in that mash to get all the sugars out. That's the all-grain part and you end up with wort (sweet liquid).

You then boil the wort for an hour or so, adding hops at specific points (for bitterness, flavor, and aroma). You then chill the boiled wort, transfer to a primary fermenter (usually a plastic bucket), pitch yeast, and wait for a while.
After a week or two, you transfer from primary to secondary fermenter (usually a glass carboy). After a few weeks in secondary, the yeast should have finished its main job and you can bottle. After a week or two in bottle, the beer is ready to drink. If you have a kegging system (with those 5-gallon kegs that were used for soft drinks), you can get the beer carbonated within minutes instead of weeks.
Some beers don't need to be transfered into a secondary fermenter and might even be ready to bottle within a few days. But it's safer and usually better to do a secondary fermentation.
Palmer's book (available online) explains most of these techniques well enough. And all the brewing books you could buy will give details on every step of the process.
With all of this, sanitation is quite important, especially after the wort has been boiled. But we all do a few things that aren't completely sanitary and scrapped batches are quite rare.
Among brewers, the motto is "Relax, Don't Worry, Have a Homebrew!"
Again, brewing can be a very nice "Flow" experience. It can be intensely creative and it relies on a scientific basis (enzymatic reactions, use of gravity, etc.). Plus it can be very social.
While it's easy to go overboard with equipment or ingredients, homebrewing can be quite cheap an activity. IMHO, it's quite easy to get started for less than 100USD and then get more equipment as we go on. Brewing with other people, it's often possible to cut costs by sharing equipment or doing bulk orders. Without cutting costs too much, I think I can brew a batch for 1USD/gallon, especially if I repitch
yeast (use it for several batches). On average, I'm guessing I probably spend about 7–10USD for a 5 gallon batch as I use a bunch of specialty grains, expensive yeast packages, and some spices. The larger the amount brewed, the cheaper the gallon will be, for many reasons (including the cost of bulk ingredients, the energy costs (fairly minimal anyway), and "mash efficiency" (the proportion of sugar
extracted from the grain)).
Of course, that's not counting the time spent brewing. Some people say
it should be counted but then one would need to "deduct" the experience
gained and the relaxation coming from brewing…
In my mind, it's a very enjoyable activity which has brought me a lot
of nice things in the last four years.

Cheers!

AleX