Always make a branch to work on, you can always throw it away if it doesn't work.
Go into your folder of projects:
> git checkout -b myawesomebranch
This creates a branch and checkes it out, you are now inside of this branch.
do your work
when ready to save it
> git add .
> git commit -m "i just did awesome stuff on this branch"
> git push origin myawesomebranch
You can show your instructor or mentor the branch
If you decide to keep it and merge back to master
> git checkout master
> git merge myawesomebranch
If you want to delete a branch on github you can go to the web interface and delete it. That is the most straight forward way :)
To delete a branch on your computer
> git branch -d myawesomebranch
Note: you can't delete a branch you are on :) doh :)