You should be able to do this directly from Android studio.
The easiest way is going to the bottom right corner of the Android Studio window where you should see the text “Git: branch name”, in your case it should say “Git: master”. Click on it and it will show a small menu consisting of the different branches available both locally and remotely, also there should be an option “+ New Branch” which will create a new branch for you and switch you to it.
You should then be able to change some code, commit it and push it to remote. Merging and checking out branches can also be done from that same menu. The same thing can also be done from the menubar option “VCS”