Don't know much about this Roku.
Can I just buy one, hook it up, and then watch this Billiard channel?
Or are there monthly fees?
You just need an internet connection and a router to stream from. There are several different models out there. I have the Roku 3 and I'm quite happy with it. It even lets you plug a headphone into the remote (with volume control) and the remote will work from any room in the house.
The Billiards Channel is free and you'll find lots of other free channels that you've never seen or heard of before and others like HBO-GO, YouTube, Vimeo, ect... (HEY WHEN ARE WE GONNA SEE THE AZB CHANNEL?).
They do have Netflix and the other pay movie channels (that come with a fee) but you'll be surprised how many free channels there are. Some channels will require you to input a code through your computer to verify your Roku, but that's a one time thing and it only takes a minute or less if you have a wireless laptop or tablet handy. Most channels (The Billiards Channel included) don't ask for a code. (The code input thing is simple).
Just remember, you are streaming off of your internet so if you have a bandwidth cap limit (AT&T... ripoff... cough... cough...) then if you steam all of the time you may find yourself with an up-charge at the end of the month. For instance AT&T has a limit of 150gb for DSL and 250gb for their U-verse. The average person won't get hit with an overage on 250gb but you can run up 150gb easy before the month is out if your not careful. You may know about all of this but I'm just throwing it out there because it's the catch in the word "free" in regards to streaming video.
But to answer your original question... if you are already streaming internet through your house then yes... just buy one, easy HDMI hook up, and you're all set to watch The Billiard Channel. But if you don't own one yet you will probably get sidetracked along the way searching through over 1000 channels. (a lot of them are junk channels). Enjoy.