If you're on a Mac (and this probably works the same on a PC), here's a very easy way to do this. Strangely enough I've looked high and low for this simple process and never found it.
- Do not do anything on Github (other than having an account, and not having used up all your available repos).
- Download GitHub for Mac and install. Go through the account setup, etc. Do NOT create any repositories for your existing project.
- "Add New Local Repository" in repositories.
- Select your existing folder. It'll ask if you want to do that, say yes.
- Once done, you'll see a list of all your files, etc. Commit them.
- Go to Repositories and Publish (this will create the new repo on GitHub for you, if you set up your account properly).
- Go to Repositories and Push (you'll either see the "nothing to push" thing, or it'll push your files/changes to the newly-auto-made repo).
- Wonder why you could not find this simple process anywhere else.
I know it is not recommended to use the project folder as the repo folder. I do it all the time, it always works, it makes it simple, and I never have any trouble with it.