How do I clone into a non-empty directory?

In the following shell commands existing-dir is a directory whose contents match the tracked files in the repo-to-clone git repository.

# Clone just the repository's .git folder (excluding files as they are already in
# `existing-dir`) into an empty temporary directory
git clone --no-checkout repo-to-clone existing-dir/existing-dir.tmp # might want --no-hardlinks for cloning local repo

# Move the .git folder to the directory with the files.
# This makes `existing-dir` a git repo.
mv existing-dir/existing-dir.tmp/.git existing-dir/

# Delete the temporary directory
rmdir existing-dir/existing-dir.tmp
cd existing-dir

# git thinks all files are deleted, this reverts the state of the repo to HEAD.
# WARNING: any local changes to the files will be lost.
git reset --hard HEAD

A slight modification to one of the answers that worked for me:

git init
git remote add origin PATH/TO/REPO
git pull origin master

to start working on the master branch straight away.

This worked for me:

git init
git remote add origin PATH/TO/REPO
git fetch
git reset origin/master  # Required when the versioned files existed in path before "git init" of this repo.
git checkout -t origin/master

NOTE: -t will set the upstream branch for you, if that is what you want, and it usually is.