You will need to look at your main code page to follow the instructions in the Creating and deleting brancheswithin your repository article. You just pull down the branch selector and type a new branch name and it will give you the option to create that branch.
I have the same problem now, or rather a related problem perhaps. I had followed the documenation but there isn't such a link for a new branch. I suspect this might be a permission thing (I'm trying to create a new branch in someone else's repo to then submit a PR), but the documenation I've seen doesn't tell you how to address any problems you might face as a new contributor to github. I've seen this generally - it would be great if more guides with troubleshooting could be added to help avoid the "it's hard to conribute" problems the community experiences (sadly I'm not in a position to do this seeing as how I am _having_ these problems myself still.