It sounds like you could use some more education on how Git works. http://gitready.com/ is a good resource for this, as is http://gitimmersion.com/ .

That said, for your specific question -- I assume you have your local repository connected to the remote one that has the "master" and "develop" branches (in this case, probably GitHub)?

If so, then you simply need to check out your develop branch, make your changes, and push them up to your server. Once you're ready to deploy to master, you merge develop onto master, and push the master branch up.

How you get your develop branch locally:

git fetch origin
git checkout -b develop origin/develop

Now, you'll be on branch "develop," which maps to your remote "develop" branch. The above assumes that "origin" is the Github repository. If you get an error, you'll need to add your Github repository as a remote with:

git remote add origin [GitHub repository url]

You don't need two separate clones of your code to handle Git branches, because Git works off of an index system. It keeps track of which branch has what. When you want to change branches, you simply check out the one you want (using the "-b" switch if it's a new branch).