Painful does not begin to describe how laborious it seems, after using more modern kit.
It appears that the AMD K6-II instruction set is a superset of that used on the i586 series. Some folks seem to be still running such, and we have a number of resolved bugs in the tracker, detailing various ways to get the units running
Based upon exhortation and advice in the CentOS QA mailing list and some IRC banter, I was induced to drag one of these poor exhausted clunkers out of my boneyard, and do some testing on it
These installation instructions SHOULD work on i586 as well, but I no longer have an examplar to confirm with:
- Download and install using 4.5 i386 ISO from vault.centos.org and start it up the following options
 Boot it with: i586 text nomce
- Manually install openssh-server, enable, and set up with iptables, so you can hop on the unit from a remote box to work on it
- Add to /etc/yum.confexclude=kernel* 
- Perform a general run updates against the intervening changes prior to 4.8 -- (seemingly 4.7 and intervening updates when I perform this testing) -- lots there, but get it close to current.Install 6 Package(s) 
 Update 150 Package(s)
 Remove 0 Package(s)
 ... took forever as I only have 128k ram for this old beast --- 308 transaction steps
- Do an interim reboot
- Point at my local mirror of the CentOS 4.8 release test candidate and let it rip -- first pass only: 
 ftp://ftp.first.lan/pub/mirror/centos/centos-qa/CentOS/4.8/os/i386/
 without the later pending updates:
 ftp://ftp.first.lan/pub/mirror/centos/centos-qa/CentOS/4.8/updates/i386/Install 1 Package(s) 
 Update 83 Package(s)
 Remove 0 Package(s)
 Total download size: 117 M
- Do a second interim reboot
 Mysteriously, I got an 'unclean shutdown' FSCK required message as to /boot here ... no idea why
- Run yum again, for a second pass with the updatesInstall 0 Package(s) 
 Update 9 Package(s)
 Remove 0 Package(s)
 Total download size: 9.8 M
- Do a final interim reboot
- I completed by my test suite without incident
I am advised similar steps may work from later than a CentOS 4.5 ISO, and that i586 should work as well. As I lack the hardware to test this, your mileage may vary
Poor old boxes. Let them rest. Save power. I need a shower. Yuck
 

 
