[git] What's the proper way to "go get" a private repository?

You have one thing to configure. The example is based on GitHub but this shouldn't change the process:

$ git config --global [email protected]:.insteadOf https://github.com/
$ cat ~/.gitconfig
[url "[email protected]:"]
    insteadOf = https://github.com/
$ go get github.com/private/repo

For Go modules to work (with Go 1.11 or newer), you'll also need to set the GOPRIVATE variable, to avoid using the public servers to fetch the code:

export GOPRIVATE=github.com/private/repo