Tested on a Windows 10 Pro machine with Windows Subsystem for Linux (WSL) installed.
In essence, a fairly vanilla installation of WSL and Docker Desktop (Community Edition of Docker is fine), as described in this article will suffice (although it may require the odd reboot).
In essence, the Docker server runs on the Windows side under Hyper-V and the Docker client is on the Linux side and connects to the Docker server side via setting the $DOCKER_HOST environment variable. As soon as you can connect to the Docker server, for example with docker ps, you can run all the instructions above in WSL.
Note 1 Using ConEmu or another tabbed console makes the "Extra Credit" section rather more convenient (and is recommended in any case, to get away from the limited console which ships with Windows).
Note 2 WSL 2, currently available in Insider Windows builds, should allow Docker to be run entirely on the WSL/Linux side. For details on installation, see this article