Dave Caolo of 52 Tigers explains how to create a new note using Siri:
To create a new note, tell Siri, “Create a new note,” “Make a new note” or something similar. You can give a note a title at the same time, for instance, “Make a new note packing list” or “Create a new note places to visit.” That becomes the first line of the note.
Updating the note using Siri is also quite easy according to Caolo:
Updating a note is easy. Simply say, for example, “Update my note toothbrush, deodorant, book, tickets, camera.” If you’ve got more than one note, Siri will ask which note you’d like updated by providing a list. Either tap the one you want to update or speak its name (the first line). If you know exactly which note you’d like updated, let Siri know. “Update my note packing list charger mouse.” Finally, get a quick look at your notes by asking Siri to list your notes.
As Caolo points out, Siri cannot delete a note or cannot be used to share a note via email (which is possible via UI). But it is always nice to know you can do few more things with Siri with the assumption that Siri can understand what you are saying.
Hat tip to Jim Dalrymple of The Loop!