Given that Linux is more or less the home os of Emacs it presents us with the most installation options. Of course, you can build Emacs from source on every distribution out there, but why bother to do so? Using the distribution’s package manager is a better idea for many reasons - you don’t need to install a build chain and lots of dev libraries, you get updated versions when they are released and you get automated dependency manager, just to name a few.
That said, few distributions include in their primary repositories builds of Emacs 24. Luckily there are some unofficial repos that come to the rescue.
Debian users should look no further than the amazing emacs-snapshot APT repo. You’ll find installation instructions there for all the relevant Debian versions out there. High quality, highly recommended builds! After you’ve added the repo you can install Emacs 24 with the following command:
$ sudo apt-get install emacs-snapshot
Ubuntu users have easy access to Emacs 24 as well:
$ sudo apt-add-repository ppa:cassou/emacs $ sudo apt-get install emacs-snapshot
Gentoo users have even less to do, since Emacs 24 can be obtained via the emacs-vcs package in portage, as noted in the official Emacs on Gentoo page.
Slackware users can compile and install Emacs 24 by using the following unofficial SlackBuild script: emacs.SlackBuild.
Unfortunately they don't seem to be any prebuilt Emacs 24 packages for any of the RPM distros (Fedora, SUSE, Mandriva, etc).