I have become responsible for a Windchill 9.1 system, but do not have any experience supporting Windchill or Oracle either. I have successfully cloned my production server into a Hyper-V VM and have been trying to figure out how to move Windchill from the 32 bit Windows 2008 server its on to a 64 bit Windows 20098 R2 system. I found the WIndchill Rehost Guide, and do not understand how to follow it.
Can you recommend tutorials or guides I can go through with the ultimate goal of being able to perform this migration?
Your best resource is to read the administrator guides to Windchill. They should be available on ptc.com for 9.1, though administraion isn't that much different in 10.x.
Since you want to move from 32-bit to 64-bit, your only choice is to install an OOTB system on 64-bit and then dump the data from the 32-bit systems to backup files and import into the 64-bit system. You will need to backup the Oracle DB, the LDAP, the cache vaults and the file vaults. You can also copy over the *.config files that your site has modified, most likely only the site.config will be needed as the others will be built when you do the OOTB install.