Food & Water
Regardless of what species of tarantula you decide to keep, it will need both food and water. Tarantulas get a lot of the water they need from their food, but a water dish is still a good idea for most species and some (mainly arboreals) will benefit from occasional misting on the walls of the enclosure.
Tarantulas are nocturnal predators and their diet mainly consists of small invertebrates. There are many available food options and what you decide to feed your spider will probably depend on local availability and cost. Young tarantulas should be fed 1-2 times per week and adults every 1-2 weeks. For a medium-size adult tarantula (5"-6"), a good average amount of food is about 2 crickets per week.
The most readily available form of food is crickets, which can usually be purchased at a pet store, bait shop, or even at some Wal-Marts. As long as they are kept in a dry, well-ventilated container, they can live for several weeks. They can be fed dry food such as grits, bread, fish flakes, or oats. A water source is needed and I've found that using some type of water crystals (purchased as a make-your-own packet) works very well, as it gives the crickets the moisture they need without the worry of them drowning.
Roaches have become an increasingly popular food source due to their long lifespan and overall ease of husbandry. There are many different species of roaches available on the Internet and it is important to do research on the different types of roaches before making a purchase. I personally use lobster roaches (Nauphoetra cinera) because they breed very quickly and allow me to always have multiple sizes available for all my spiders. I keep my roaches in a large Rubbermaid container in a corner of the room. There is no noticeable odor and extremely little noise.
Mealworms / Superworms
Mealworms and superworms are both appropriate tarantula food. Both can typically be purchased either online or at a pet store and require little upkeep. Mealworms should be refrigerated as to slow growth and increase lifespan. Superworms should be kept at room temperature. If you choose to feed mealworms or superworms, it is good idea to crush the head before giving to your tarantula to keep them from burrowing into the substrate.
Other appropriate food for tarantulas include locusts, moths, termites, and other small invertebrates. I recommend against using insects that you can find in your backyard unless you are certain that they have not been exposed to pesticides.
Some tarantulas will also eat small vertebrates such as pinkie mice and anoles. Vertebrates are not a necessary part of a tarantula's diet and your spider will do well without them. However, if you choose to feed vertebrate prey, I highly recommend pre-killing the food to prevent it from fighting back and potentially harming your spider.