To edit an existing Lead note, click on the Edit icon for that note (a note can only be edited by the user who created it):

Your note will open in edit mode and you can now update it. 

You can change the text of the note, stick the note to the top of the list, insert new images, delete existing images (or change their labels), and select users to be notified about the changes:

After you've finished editing the note click Save and the changes will be saved. Also, a confirmation message will be shown in the top right corner: 

If you attempt to leave the page or close the browser tab while the note is still open in edit mode, a warning message will be shown asking you to confirm if you wish to discard your changes:

After your changes have been saved, an additional icon will appear on the note, which enables you to view the note's edit history:

After you click on the Edit History icon a popup will appear showing your note's history including a preview of the changes, the user who made the change and the date and time of the change.

Text deletions are highlighted in red color while new additions are highlighted in green:

The text changes will also be highlighted in the note email notifications (in case you selected users to be notified of the new edits):