On a Contact Profile, Notes can be added, deleted, and searched.
To add a note on a contact profile, open the profile, scroll to the bottom to the Notes section, add the note you want in the window, and select Save. The note will be saved.
To delete a note, you can only delete your own notes, not those of other users. Also, you must have the proper permissions. If you look at the Notes section and see a trashcan icon to the right of the note, then you have the correct permissions. If not, either this is not your note to delete or you do not have permissions to do this.
To search notes, this is part of the Boolean feature of Contact Search. Go to the Talent Community section and in the Boolean Search information below the search window, that document tells you that the Boolean Term for searching notes is notes.comment.
Also in that Boolean document, it gives hints as to the types of searches you can perform:
For Notes searching, you need to know that whatever you type, the search will look for exactly that. For example:
will look for the exact Notes entry 'Test contact'.
Hence, if you want to look for a word or phrase that might be part of a larger entry, you will want to use wildcards.
will look for the term 'Test contact' as part of a larger entry.
Notes searching is not case sensitive, so notes.comment:*Test contact* is the same as notes.comment:*test contact*.