There are many materials necessary to brew, and some of them can be expensive. Restaurant supply stores and home brewing stores will have what you need. Here are the basics:
A large boiling pot
It must be made of stainless steel or ceramic-coated steel. The bigger the pot the better, because it needs to be able to hold at least 3 gallons of liquid with room to spare.
One 5-gallon carboy
A carboy is a large, glass bottle. They look identical to the bottles that large amounts of water are often sold in, but they must be made of glass for beer brewing. Visit your local recycler and ask if they have any on hand to sell, as they are expensive to buy when new.
Funnel
You will need a large funnel to transfer the wort into the carboy.
A 6-gallon plastic "bottling" bucket with lid
This plastic bucket should hold at least 5 gallons and be food-grade. You can find them cheap (or free) at many restaurants; ask the kitchen staff to save any extra for you rather than throw them away.
Siphon hose
This is at least 6 feet of plastic tubing that will be used to transfer beer from the carboy to the bottling bucket, and later into bottles.
Racking cane
An ingenious piece of shaped, hard plastic tubing that connects to the siphon hose for transferring beer from one container to another.
Fermentation lock (airlock)
This clever feature will seal your beer from outside contamination while letting carbon dioxide escape the fermenter. It must fit in a hole in the lid of your carboy.
Long spoon
This will be used for stirring; make sure it has a long handle so you don't get burned.
Bottles
Do not use the type with twist-off caps. Any type of sealable glass bottle is good: beer, old-fashioned pop or even champagne bottles. Ask your friends to save these types of bottles for you.
Bottle-capper
It is used for securing caps onto bottles. You can use any style that catches your fancy.
Bottle caps
For capping your bottles.
Household bleach or an iodine solution
Used to sanitize brewing equipment (2 ounces bleach to 5 gallons water).
Thermometer
Be sure to use a thermometer that has a range of at least 40 degrees F (4 degrees C) to 150 degrees F (65 degrees C). Either a floating dairy thermometer or a stainless steel dial thermometer can be used. The floating dairy thermometer can be broken more easily than the stainless steel dial thermometer.
Put your equipment to work! See Beer Brewing for Beginners.
Keep it Clean
Always start with a clean workspace and sanitized equipment. You can use either a bleach solution or an iodine solution to sterilize your equipment.
Bleach is readily available and inexpensive. The downside to using bleach is that chlorine can leave an unpleasant, chemically aftertaste: either rinse well with boiling water, or allow equipment to air dry several hours before you begin. Use half an ounce of bleach (1/2 tablespoon) per 1 gallon of water.
For a beer brewer's iodine solution such as iodophor, iodine is combined with other molecules in order to make the iodine safe for kitchen use. This solution is easier to use than bleach, because it does not require additional rinsing. The proper dilution ratio for iodophor can be found on the bottle, available at home brewing supply stores.
Fill your racking bucket with tepid, not hot, tap water and the appropriate amount of sanitizer. Place brewing equipment in the bucket and let it soak for approximately 10 minutes. (If you are using bleach, be sure to bring a large amount of water to rapid boil for rinsing your equipment.)
Use a spray bottle filled with the diluted sanitizing solution to sanitize the countertops and any surrounding work areas; let air dry.
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