Good espresso is perhaps the most difficult coffee drink to create in the home. When we examine the other popular forms of extracting flavor from the humble coffee bean, we find classic drip, which can be easily screwed up, but which is easily enough done properly if one has a machine which brews to the proper temperature. The very inexpensive ones don't but there are a number of them which do, and are commonly available over the counter at Wal-Mart or Target. The delightful french press or press pot is a simple device which only requires a properly coarse grind. A coarse grind is pretty easy to do on a $50 conical burr grinder. When we look at Turkish/Arabic/Greek coffee, we have to get a very fine grind indeed, but the process is fairly simple from there.
Espresso, however, is a bit more complex. With every other brewing method, the three major variables which the brewer must be concerned are: temperature, grind, and steep time (the time in which hot water is actually in contact with coffee). To this mix, we add pressure, and consequently flow rate when speaking of espresso. Since we pack the coffee into the portafilter and force hot water through the bed of grounds for a short time, all the factors which we must be concerned with before, along with the new ones added, are magnified in importance. There is little margin for error. A slightly more coarse grind must be made up for with more tamping. This is the method utilized in what is known as Australian updosing. An overly fine grind will probably clog the portafilter and you will get a few wimpy drips, rather than the steady pour with thick, sienna colored crema. Therefore, unlike the other brewing methods, extreme care must be taken in the choice of equipment for even acceptable results. You are going to spend more money on equipment making espresso than you will making coffee via the other methods mentioned above.
The first thing to get is the grinder. It must be conical burr, and not just any old conical burr. Espresso is a very fine grind. Many of the less expensive grinders will not do the job. Prices start at about $150 for the entry level machines. You can easily spend $1000 on a grinder for espresso. Don't laugh. When the unfortunate obsession grips you, dear reader, it clutches you with a zealous grip. Blade grinders, by the way, aren't really useful for grinding the best coffee. They can do a pretty bang up job on spices, though! They grind unevenly, and you end up with what is known as boulders and dust. There is, fortunately, a way to get around the need for expensive equipment, but you will sacrifice convenience for your frugality. Remember when I mentioned that Turkish/Arabic/Greek coffee required a very fine grind? Well, that grind is just about coffee flour. There are two ways to do this popularly; a mortar and pestle or a stone wheel (which works the same way), or a Turkish mill. A Turkish mill is a conical burr grinder which substitutes the electric motor with a hand crank. They are usually adjustable, and since they must be capable of grinding the aforementioned coffee flour, they can frequently do a good job with espresso, which is not so fine a grind as that. I got one off ebay for 15 bucks, shipped. It does a fine job (I'm the only coffee lover in the house, apart from my 6 year old daughter, who gets the occasional decaf milk drink). Espresso enthusiasts will tell you to spend most of your money on the grinder, as this has a greater effect on the quality of the espresso than the machine. So, that takes care of the most important part, the grind.
The choice of machine is very important as well. Modern espresso is made with a pump and hot water. In the old days (and lo! giants were in the earth), espresso was made with steam, which was forced through the coffee at a couple of atomospheres of pressure. This burned the coffee, unfortunately. Nowadays, espresso machines have a pump to force hot water (around 95 degrees C or so) through the grinds. There are a lot of them on the market. The best ones use a boiler rather than a thermoplate to heat the water. Ideally, there should be one boiler for the grouphead (where the coffee comes out), and another for the steam wand (the attachment used for frothing and steaming milk for lattes and cappuccinos. That way water can be held at a lower temperature for the coffee and a higher one for the steam. Decent machines start in the same range as decent grinders, but you won't really get temperature stability until you spend about $400-$500. You can shoot the moon here as well. A 4 group La Marzocco could set you back $10000.
A word should be spoken on the roast. Traditional espresso uses a very dark roast, but espresso can be enjoyed at any darkness you wish. In fact, the flavor of the actual bean comes through better in lighter roasts. I tend towards a full city roast myself, but you should experiment in this regard to determine what suits your palate. Good espresso does not require sugar. Bitter espresso is a sign that something went wrong with the extraction process, usually. Sour espresso usually means old beans. You really want beans wtihin a month of the roast. Preferably within 2 weeks, really. The first couple of days after roasting, beans will generate a lot of froth because they are still de-gassing. Don't pre-grind espresso. Coffee loses a lot of aromatics within minutes of grinding. Espresso is really meant to extract the maximum flavor from the beans, so you will lose something noticeable if you grind the beans at the store and bring them home. Regarding the type of bean, since espresso is a very concentrated drink, blends work well. A good espresso has a lot of different flavors going on in that 2 or so ounces (in a double). Espresso blends may have 3 or more types of beans. There are single origin espresso beans, but they tend to be beans which provide a variety of flavors.
Wertperch messaged me remarking that he got a stovetop espresso pot. Stovetop espresso is also called a moka pot. Basically, you heat water in the bottom, and this heat forces the water through a bed of ground coffee in the middle into a reservoir at the top. It produces similar coffee to steam espresso, but does not burn the coffee so much, so is to be preferred. The resulting coffee, while not true espresso (and believe me, good enough for government work is not a saying among the hardcore coffee aficianados), is nonetheless, a very good cup o' joe. Since these things can be found for as little as 5 bucks at Ross for Less (yeah, I looked), you might find this a suitable substitute for an expensive machine. If you like good coffee, and not a specific idea of what you should have, you should use your own tastebuds to determine what you like.