To export a single file from a remote:
git archive --remote=ssh://host/pathto/repo.git HEAD README.md | tar -x
This will download the file README.md
to your current directory.
If you want the contents of the file exported to STDOUT:
git archive --remote=ssh://host/pathto/repo.git HEAD README.md | tar -xO
You can provide multiple paths at the end of the command.