You don't need to use Github with PHPFog. PHPFog hosts git repos for you. In the code tab of your app's details, in the PHPFog web console, you will see how to clone down your app. The command will look something like:
git clone git@git01.phpfog.com:myexample.phpfogapp.com
Running that command will clone the app down into a folder named myexample.phpfogapp.com
Next I would move all your project files from your current folder into this new folder. Once you made your file changes and are ready deploy, change directory to the new folder and run the following commands.
git add .
git add -u
git commit -m "Initial commit"
git push
If you run into any "fast forward" errors pushing use the --force switch
git push --force
Another way to do this without the clone would be to initialize a git repo in your current folder and add the PHPFog repo as a remote:
git init
git remote add origin git@git01.phpfog.com:myexample.phpfogapp.com
git add .
git add -u
git commit -m "Initial commit"
git push --force
Side note: you can use Github as an additional remote repo if you want to but its not necessary.