To be able run 32 bit application on 64bit version of Archlinux, you need enable multilib repositories. See here for setting up. Then install basic 32bit libraries.
$pacman -S lib32-glibc lib32-ncurses lib32-libstdc++5
Now try run some 32 bits application. For this example i'm running Android SDK that only available on 32bit version.
By default android SDK Application only available 32bit version. If you didn't install this library on 64 bit system, android sdk apps will not running. Here's some snapshot of ddms applicaton (part of android SDK)
And also you can run Fastboot and adb on Archlinux too. For another 32 bit application that available on official repository, if you enable multilib, then the librari 32bit will be installed for that application automaticly.
And also 32bit application from AUR, if you do makepkg -s, the needed librari will be installed too. So it's simple. :D