I've run the HCK test suite (haven't tried the HLK, yet, bu from what I recall reading, the setup is similar). Basically, you need 2 servers, one to run HLK Studio and the Controller, and the other to run the HLK Client where the driver will be tested. Under HCK, the servers have a network connection.
You use the Studio/Controller UI to select and configure the tests and to find and select the driver on the remote server to be tested. Selecting tests is a bit odd on a software-only driver, but through trial-and-error and a lot of reading, I was able to find an appropriate set (it's a file system minifilter).
Once you start the tests, go find something else to do - the tests ran for about 12 hours in my case.
When you come back, you have to very carefully use the UI to collect the driver and the test results into a package file. You separately sign the package file with a cert that has been previously submitted to Msft (so they know who signed the package), then use the UI to upload the package to a Msft URL.
There's a website where you can view the signing process - it goes through several stages. In my case it took anywhere from 10 minutes to a few hours to get through all the stages. At the end, if all goes well, you'll be able to download a zip file that contains your driver signed by Msft. Once you have your driver, put it in an installer (we used WiX [0]) along with any other components (like a nice userspace tool for configuration, or to run as a service and load the driver to do useful things)
For a software only driver, it's a lot of busy work. I really don't think the HCK exercised my driver at all. Nevertheless, either me or the release engineer at work got through the process several times.
[0]: https://wixtoolset.org/