There are three types of notes you might add to a contact. The first is a note directly on their person. The second is a note on a task (that is associated with their person) and the third is the record of an Interaction.
To add Notes on a Person click on the People menu in the left navigation bar or search for their name in the search bar at the top of the page.
Select the name of the person.
In the middle section of their page, select the Notes tab.
In the Notes tab, select Create New Note.
Record the Note Details in the available field. The Visibility of the note will default to "Hidden From Viewers" and will not be shown on the person's timeline.
Select Save and the Note has now been added to that person.