I keep fixing this up, but if it fails for you, check if these are better maintained https://tip.golang.org/cmd/go/#hdr-Configuration_for_downloading_non_public_code and https://golang.org/ref/mod#private-modules.
Cloning the repo using one of the below techniques should work correctly but you may still be getting an unrecognized import error.
As it stands for Go v1.13, I found in the doc that we should use the GOPRIVATE variable like so:
GOPRIVATE=github.com/ORGANISATION_OR_USER_NAME go get -u -f github.com/ORGANISATION_OR_USER_NAME/REPO_NAME
The 'go env -w' command (see 'go help env') can be used to set these variables for future go command invocations.