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.