Step 1: Before you start to stream you first must make sure your channel is "created" on TwitchTV. When you initially signup, only an account with your name is created, not your channel yet. You can "create" your channel visiting your TwitchTV Dashboard once.
Step 2: You need to decide what you want to stream. Will you be streaming PC games or console game? If it is a console game, you will need some form of hardware capture card as well.
Step 3: Does your PC have enough power and sufficient upload throughput to steam. Ideally, you will want a Core i5, i7, or a recent model AMD processor and ideally atleast 1.5 - 2 Mbps upload if you want a high quality steam. Although, depending on what you are streaming, a slower processor may work too. If you are streaming a PC game, you will also want a decent graphics card as streaming will place an increased strain on your system.
Step 4: Decide on a streaming application. Your main options are XSplit (free and paid), OBS, FMLE, and FFsplit. XSplit, OBS and FFsplit includes built in desktop capturing while FMLE requires a 3rd party capturing software such as SCFH DSF. We recommend starting with XSplit if you are new to steaming or OBS if you are looking for a totally free solution.
Step 4: Set up your streaming software. There are already a large number of really good guide for this so I will just link them here. The basic steps include creating your connection to the TwitchTV server, configuring your quality and bandwidth settings, and configuring a capture of your desktop (PC) or from a capture card (console).