With a clean master branch checked out, you can create a task branch by typing:
git checkout -b task_branch
where the task_branch is the name of the branch you want to create. By using the -b option it will both create a new branch and check it out.
As your are doing work you can commit regularly, and you must also commit when you are finished with your task. You can commit by typing:
git commit -am "commit message"
and you should leave a detailed commit message describing the changes you made.
Now that you've finished your task you need to checkout master and merge your work. To checkout master simply type:
git checkout master
and to merge your task branch type:
git merge task_branch
where task_branch is the name of your branch.
Now that your work is merged, go ahead and push the master branch by typing:
git push origin master