The Tarantula story starts way back

In 1370, in a small town called Taranto in southern Italy a strange and mysterious epidemic broke out for which the only cure seemed to be wild dancing and music. Occurring every summer for three hundred years, this disease was thought to be caused by the bite of a large, hairy Wolf Spider (Lycosa tarantula), which became known as a Tarantula.

In the 1600s, people discovered that these spiders were virtually harmless. Many then concluded that the whole phenomenon of Tarantism was simply an excuse far a wild party. However, it is now suspected that a spider was involved and the real culprit was a European relative of the Redback or Widow Spider.

As Europeans colonised the world, they saw even bigger and hairier spiders, and called them Tarantulas too. As a result, many large and hairy spiders are now commonly, but incorrectly, called Tarantulas. The only true Tarantulas are the large spiders of the family Theraphosidae.

Enclosures
The sky is the limit for enclosures. I personally like 5 gallon aquariums for larger species as they are attractive and easy to maintain. Besides aquariums, you can use large plastic jars, plastic shoe boxes or custom made enclosures. The top should be covered with screen, mesh or cheese cloth to provide adequate ventilation. It should not have any openings larger than the carapace of the spider and the top must be secure to deter escape.
Tarantulas do not require vast amounts of space and too much area can actually make it difficult to locate prey. Tarantulas are not especially sociable and should be kept in separate enclosures.

Substrate
The purpose of the substrate is to hold moisture to help maintain humidity levels and to allow certain species to construct their burrow. The preferred substrate is vermiculite, either alone or mixed 50/50 with peat or potting soil. Vermiculite alone should have water added until it has the same dampness as, say, your average garden topsoil. While some also recommend wood chips or shredded bark, there are differing schools of thought on this, especially the wood chips, and I prefer to just stick with vermiculite. Sand and gravel make a poor substrate and are generally avoided although some people like to mix it with the peat and vermiculite. Feel free to experiment!
Fill your enclosure about 1/3^rd of the way up with substrate material. This will give plenty of moisture and will also prevent injury to the spider by limiting how far it can fall if it decides to get rambunctious.

Hides And Decor
Simple is the key here. Use something that will provide shelter, such as a piece of cork bark, a ceramic pot or the like. I prefer plastic plants over live ones for the obvious maintenance advantages. Live plants may also have been treated with insecticides.
While being aesthetically pleasing, poorly thought out decor may cause injury to the spider by falling on the tarantula or the spider falling onto it (jagged rocks, cacti, etc.). If it has cracks and crevices, it may give the prey animals a place to hide. Live plants or items you find outside may be poisonous to the spider or can be infested with mites or fungus that can also harm your spider. Cedar is poisonous to tarantulas and needs to be avoided at all cost.

Cleaning
You'll find that your new buddy is quite clean. After meals, there may be a little glob of cricket (cricket boogers) and/or some legs laying around. Remove these as soon as possible as some mites will feed on them. You may also notice a whitish film on parts of the tank. This is the tarantula's excrement and can be removed quite easily with a damp paper towel. Changing the substrate need only be done a few times a year. If you notice mold, mites or a mildew smell, you (and the spider) are ready for a change.

Lighting
Tarantulas are generally nocturnal and don't require special lighting. If you wish to use light, go with small fluorescent lights. The incandescent lights get very hot and can overheat or dehydrate your pet.
Never place the enclosure where it will receive direct sunlight, the high temperature will dry out the cage and may injure or kill your spider.

Climate
Tarantulas are found on all every continent except Antarctica, and come from a wide variety of environments. It is important to know what climate your spider has come from in order provide it with the optimum living conditions. Thermometers and humidity gauges are a good idea to help you monitor the environment.

Temperature
Tarantulas, being cold blooded, acquire heat from the surrounding environment. For most, the optimum temperatures range between 75° f - 85° f (23° c - 29° c). There are many ways to ensure sufficient heat ranging from a heating pad placed 1/3^rd of the way under the tank, to heat rocks and even climate controlled rooms for the larger collections. Incandescent lights should be avoided as they tend to be overly drying and the constant light can upset the normally nocturnal tarantula.

Humidity
The humidity of the cage is every bit as important as the temperature. Even tarantulas that come from dry environments seek shelter in more humid burrows and come out at night after the desiccating sun has set. Humidity levels should be maintained at 60%-90% and should never drop below 50%. You can easily lose your spider during a molt and I have heard of problems with the lungs drying out if the humidity is maintained too low.
The easiest way to maintain humidity is by keeping the substrate moist. The nice, even evaporation rate ensures a consistent humidity level and with adequate ventilation, you should have no problem with mold or mites. You can also lightly mist the inside of the cage once every week or so to help maintain humidity.

Food & Water
Many owners feed their tarantulas once every 1-2 weeks. Lately I have had mine on a very erratic schedule trying to mimic the randomness in which a spider might find food in the wild. I will feed one cricket, two weeks later three crickets another cricket in three or four days, etc.. You get the idea, there's no real pattern and I never think very hard about when I'll feed them next or how much. Spiderlings, which are growing faster and molting more often should be fed two to three times a week.
While most keepers keep their tarantulas on a diet of commercially or personally raised crickets, you can also offer your spider other insects, small mice, lizards or other prey items as long as you feel that the tarantula can safely handle it and not end up as a meal itself. There is no documented proof that tarantulas actually need a varied diet, but hey, it sure can't hurt. Food items not eaten within 24 hours should be removed and sent back to tell cricket horror stories.

Be cautious when catching food in your yard or garden, as wild caught insects can be infested with parasites or even worse, be contaminated by insecticides.

Prey items should be kept well fed and watered to insure a your spider is getting the maximum nutritional and moisture benefits from it's meal. I feed my crickets dog kibble as well as small amounts of kitchen scraps ranging from breads to fruits and veggies. I keep a fresh supply of water in a dish filled with cotton balls to avoid drownings.

Water is essential for all life and your tarantula is no exception. Tarantulas can get moisture from prey items, the substrate and the ambient humidity. Additionally, you should offer a small open water that is just deep enough to drink from but not drown food items. Place a sponge or a rock in deeper dishes.

Molting
Like insects, tarantulas have an exoskeleton that provides protection and support, but doesn't allow for growth. Molting is the process by which your spider sheds it's outgrown skin, replaces missing or damaged appendages and replenishes it's hair (eat your heart out guys!). Adults will only molt once or twice a year, but growing spiderlings will do so quite regularly.

Handling
Many species of tarantula cannot be handled safely and even the "docile" ones are wild animals that have the potential of delivering a painful bite. Children absolutely should not be allowed to handle tarantulas and I personally don't recommend handling tarantula's in general. Handling introduces the potential of being bitten, or the danger of dropping the little guy/gal causing a fatal "splat". Less serious problems include skin irritation or allergic reactions to the urticating hairs on the abdomen and the possibility of the spider escaping or climbing on you in a way that makes it difficult to retrieve.

Personally, my spiders, which are quite docile, are handled so infrequently that they have become accustomed to only food items entering their turf. This means that as far as they are concerned, anything entering the enclosure is lunch until proven otherwise. If I wish/need to handle them I have to gently nudge them with a wooden dowel which is usually attacked at least once. After they realize that the current intrusion is not a meal, I am able to handle them.
 
If you must handle your pet, knowing the tarantula's body language is highly important. When mildly annoyed, the New World species, such as we are talking about here, will often "throw" urticating hairs by rubbing their abdomen with a back leg. This behavior can be roughly interpreted as "buzz off" and it is usually just as well to heed the advice. A more serious sign is when the spider rears up with it's front two legs in the air, it may even tap you with it's front legs. The spider is now telling you that it feels very threatened and will bite if you don't back off. Don't call it's bluff! Back off and leave it be.