Growing hops for beer brewing requires a moderate climate, a trellis, six to eight hours of sun each day, and well-aerated, nutrient-rich soil. Hops are grown from rhizomes, which is a small root-like section of the parent plant. You can buy these online and have them shipped to you in time for growing season. They grow into tall bines, which do not use tendrils or suckers to climb, but instead grow upward in a spiral pattern to support themselves.
Once the last frost of spring has passed, choose a location that gets at least 6-8 hours of sun each day, such as the south side of your home or an exposed area in your garden. You'll need plenty of vertical space, as the bines will grow to upward of 25 feet tall. Prepare the soil by fertilizing well and turning it over several times to aerate it. Plant the rhizomes in front of a trellis or other vertical support, root side down about 4 inches deep, in a mound approximately a foot high to provide adequate drainage. Cover with hay or mulch to keep down weed growth. Keep them watered, especially in a particularly dry, hot summer.
Train the best-looking bines to grow up their trellis by looping them until they begin to spiral upward without help. Trim the rest of the bines off. By late summer, they should be ready to harvest. Dry them in a paper bag indoors for a week or two. Then they are ready for brewing. Store unused hops in a well-sealed bag, and freeze until needed.