When I run this the terminal prints out a bunch of icons that look like they are from the Matrix, and nothing is happening in that directory.

so there are two little things wrong with the line you posted. The process is fine, just two minor details:

1. it should be 'tar Jx' not 'tar xz' after the pipe, because the data archive you extracted before the pipe has *.tar.xz format.
2. Make sure you have permission to write to /tmp folder. You can overcome this by either doing 'sudo tar' after the pipe, or extract to somewhere in your home directory (eg ~/.tmp)

As an example, I just put the following in my command line and it worked (after making sure that /tmp/google-chrome exists):

I ran your command and it worked. So now I see three folders in /tmp/google-chrome/. Etc, opt, and usr. So do I just copy the folders to where they should be in /?

Yes, the reason why I put it in /tmp/google-chrome is for packaging/archiving purposes (This is how slackpkg works), also to audit the files to see if everything looks fine. If you don't care about it you could just do:

and it would extract the files into the root directory.

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How would I know the what applications I need for the program?

I'm not sure what you mean? When you extract the files to root directory it's all in place. Google Chrome executable is /usr/bin/google-chrome-stable, which is a symlink to /opt/google/chrome/google-chrome

In /tmp/google-chrome/usr/share there is a folder called gnome-control-center and in my /usr/share I don't have a gnome-control-center folder. Also in /tmp/google-chrome/etc there is a folder called cron.daily, which I don't have in my /etc.

What should I do?

Just ignore/delete them. If you don't have Gnome DE, then you're not using gnome-control-center. I believe the files under that directory adds Chrome preference tab in gnome-control-center (Never used it myself). You can safely delete the cron file too. Slackbuilds comment says the cron job is only for Debian/Ubuntu.

So I deleted the cron.daily folder in /etc and gnome-control-center in /usr/share. When I type google-chrome-stable I get an error saying I need libgconf, but in BLFS there is no libgconf? What do I do?

EDIT: I got Google Chrome running by install GConf for the BLFS list of packages

From my own notes, the dependencies of google-chrome is:

I got it working by installing gconf.

Now it's too late but why didn't you go for http://www.linuxfromscratch.org/hint...nd_pkg_man.txt

It's an extremely light concept, actually cannot be more light

In case you change your mind, I recommend you start all over again (yes that's part of the game with LFS) and you give a try to it

I will once LFS 8 is released :-)