The system I am using has no package installer in the root fs image. How do I install opkg itself? I can't find a link to the x86 binaries.
It probably doesn't exist.
According to its website,
Without knowing which distribution or version of linux you installed, it's very hard to be more specific; all I can suggest is looking at the website of whatever distribution you installed.
There aren't x86 binaries, because it's really aimed at embedded devices and the like. You'll have to compile the source yourself: http://code.google.com/p/opkg/source/browse/
It does beg the question though... If it's an x86 machine, why not just use apt/dpkg?