To install Arch Linux from another distribution, a root server rescue system or 
a live system, follow the instructions at
https://wiki.archlinux.org/index.php/Install_from_Existing_Linux. A short version
is provided below:

* Make sure your system is running Linux 2.6.32 or later.
* Extract this tarball. If you have enough memory, you can extract it into a 
  tmpfs file system. In the example below, we'll assume that you extracted it in
  /tmp.
* Enter the chroot:
  + If you have bash 4 or later installed, run
    # /tmp/root.x86_64/bin/arch-chroot /tmp/root.x86_64/
  + If you don't have bash 4, run the following commands:
    # cp /etc/resolv.conf /tmp/root.x86_64/etc
    # mount --rbind /proc /tmp/root.x86_64/proc
    # mount --rbind /sys /tmp/root.x86_64/sys
    # mount --rbind /dev /tmp/root.x86_64/dev
    (if /run exists on your system:
      # mount --rbind /run /tmp/root.x86_64/run
    )
    # chroot /tmp/root.x86_64/
* In the chroot
  + Initialize the pacman keyring:
    # pacman-key --init
    # pacman-key --populate archlinux
  + Mount the destination partition under /mnt
* Follow the Arch Linux installation guide
   https://wiki.archlinux.org/index.php/Installation_Guide#Install_the_base_system
  starting at the "Install the base system" step.