I just went through the upgrade process from TDM 3.1.2 to 3.2 and wrote up this document with the steps and screenshots I took to do so. I hope this can help some with their own upgrade.
This information can now be found in the official product documentation wiki here: Upgrade Product Components - CA Test Data Manager - 3.2.1 - CA Technologies Documentation
If you are upgrading from 3.1.1 to 3.1.2, I have attached a document outlining those steps.
The only difference is how to download the product from CA Support Online. You will need to choose the 3.2 release, and from there you will be able to download the 3.1.2 release.
Thanks Aditi for this document!