Easy and simple to use! Twitch is very resource intensive, and some of us can't run Source for things like Korean streamers with ridiculously high quality streams simply because Twitch takes up so much CPU. I didn't even know BaseTradeTV was 60fps on Source until I did this!
First, go to http://www.videolan.org/vlc/index.html and download VLC. It is a free media player.
Second, go to http://livestreamer.readthedocs.org/en/latest/ and get Livestreamer.
Install both of those, then go to Command Prompt (Press Start+R, type cmd, then hit Enter), and type "livestreamer twitch.tv/usernamehere qualityhere" without quotes, usernamehere being the name of the Twitch streamer's channel, and qualityhere being one of the quality selections (worst/mobile, low, medium, high, best/source).
There you go! And I recommend that you open their stream in your browser and pause the video so they get your view because using Livestreamer won't recognize you as a viewer.