This is done by means of a program you download. You then slurp your LJ, edit it (weed out memes and broken images and entries you'd not want to see in print and the like), upload it, choose how you'd like to have it printed, and order it. See the News post for a discount code (how snazzy).
You must register for a BookSmart account in order to download the software.
Sadly, as the EULA includes statements such as you might expect about intellectual property, pornography, and obscenity, people who write fanfiction should take a very *careful* look at this before choosing to use this to publish stuff that includes fic, and people who write smut may well be out of luck. :( BookSmart staff does reserve the right to review what you plan to print and reject it.
I'm downloading, and I'm going to see if it can take all eight years of my journal. Wish me luck!
[Edit: No, it can't.]