Create a git repo on-line (eg. github.com)

Save your Unity project on your local filesystem

Enable External option in Unity → Preferences → Packages → Repository (only if Unity ver < 4.5)

Switch to Visible Meta Files in Edit → Project Settings → Editor → Version Control Mode

Switch to Force Text in Edit → Project Settings → Editor → Asset Serialization Mode

Save scene and project from File menu.

Quit Unity and then delete the Library and Temp directory in the project directory.

Delete everything but the Assets and ProjectSettings directory.

Make your first commit. Open terminal and follow the next 6 steps.

cd to/your/unity/project/folder

git init

git add *

git commit -m "First commit"

git remote add origin [email protected]:username/project.git

git push -u origin master