There's a myriad of reasons for wanting to backup your bluray discs to your computer. For me it's so I can watch the films, in HD, with audio commentaries during my commute to work (iTunes Extras stream commentary tracks so if you're offline there's no way to listen, which to me is very stupid and Apple should just include the commentary as a secondary audio track). For others, it's to get rid of that stack of physical media their partner keeps complaining about (though, then it's not really a backup). While the legality of this process is perhaps dubious depending on where you live, the general consensus (here in Canada, anyway) is if you're backing up for personal use it's fine, just keep those rips off Pirate Bay.
This article is mostly for my own purposes, because every time I have to set up a new computer with the ability to rip bluray discs I have to search the web and go through about four different articles to piece all the information together, so I wanted to put it down all in one place to save myself some clicks. Most of the information is adapted from this excellent article by Jason Snell at his site Six Colors, but I've condensed it down to the steps I use, as well as filled in any gaps I noticed in the steps.
1. Download and install Handbrake
2. Download and install MakeMKV. Once installed, enter license key (it's free while in Beta).
3. Install Homebrew if you haven't yet (you probably haven't). It's as simple as typing this into Terminal and letting it run its course (you may need to type your admin password a couple times):
/usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"
4. With Homebrew installed, install DeCSS. Simply type the following command into Terminal (again, you may need to type your admin password a couple times):
brew install libdvdcss
5. Finally, with all the tools installed, run the following Terminal commands so that Handbrake and MakeMKV can talk to each other (did I mention admin passwords?):
mkdir -p ~/lib
ln -s /Applications/MakeMKV.app/Contents/lib/libmmbd.dylib ~/lib/libaacs.dylib
ln -s /Applications/MakeMKV.app/Contents/lib/libmmbd.dylib ~/lib/libbdplus.dylib
If you've done all the steps correctly you should be able to launch Handbrake, point it to the Bluray disc (point to the disc itself, don't open and point to the contents or it won't be able to read the disc) and backup your discs to your hearts content.