You have to be in a notebook to create a note – after you open a notebook, you should see a pencil in a square icon on the left.
If you don't have any notebooks – from Notes.LDS.org, tap on the Notebook tab (third icon from the left in the left column). Then you can use the "+" button to create a new notebook.
Samuel Bradshaw • If you desire to serve God, you are called to the work.