My Second Year Cascade Hops
Hops are an extremely resilient plant, so if you happen to lack a green thumb, you may still be good at growing hops. Hops need as much sunlight as possible, lots of water, and plenty of room to grow. If you provide the hops with these necessities, and choose a good hop type for your area, they will likely grow very well and eventually provide you with plenty of hops. When it comes to selecting a hop type to grow, I highly recommend choosing one that is known for its resiliency and is suitable for all climates. This way if your soil/climate conditions aren't perfect, you will still have a great chance of success. Another point to note is that you wont be able to tell the exact alpha acid content of the hops you grow, unless you send them off to a lab. So, to make things easier, I recommend planting aroma, or dual purpose hops. Using your hops for late additions will really let you appreciate the aromas and flavors of your hops. You won't have to worry about your bitterness calculations being off, and you will get more out of your hard work than just hop bitterness.
I have had excellent success with Cascades, and have two plants currently in their third year. They produce a great amount of hops and their resiliency is second to none. They even survived being under a few feet of salt water thanks to hurricane Sandy. To help you further in selecting what hop varieties to grow I have provided links to two very helpful guides. These will help you narrow down your hop selection based on your climate and disease susceptibility. The first is a very detailed comparison table put together by sweetcell from Homebrewtalk.com. It details preferred climates, and disease/pest susceptibility for each variety.
sweetcell's Hop Grower's Comparison Table
The second table is a more simplified list by americanbrewmaster.com
American Brewmaster Growing Hops
At this point you've probably narrowed your choices down quite a bit to hops that are suitable for your climate (or any climate) and to either aroma or dual purpose type hops. The final step is to pick a hop that you enjoy using. Once you've selected what variety(s) of hops you would like to grow, you will need to get your hands on the hop plants themselves. Most homebrew shops will let you order/pre-order hop rhizomes (piece of root that you put in the ground) towards the end of winter. They are usually shipped in beginning to mid April. While you are waiting for them to arrive, be sure to prepare an area for planting and build a trellis.
The posts below will guide you through the rest of the process.
Growing Hops at Home Part II: Building a Trellis
Growing Hops at Home Part III: Planting and Maintenance
Growing Hops at Home Part IV: Harvest and Storage