Well, It's quite easy.
Open your local project.
Add a README.md
file (If you don't have anything to add yet)
Click on Publish on Github
Choose as you wish
Choose the files you want to include in firt commit.
Note: If you don't select a file or folder it will added to .gitignore
file
You are good to go. it is published.
P.S. If this was you first time. A prompt will ask for for your Github Credentials fill those and you are good to go. It is published.