Hi Jbro!! Welcome to Apple Support Communities! I understand that you have questions about the notes application and I think I can help with that. Theres lots of great features within the Notes application, continuity across devices is certainly one of them. First things first, make sure you are signed in to the same Apple ID on the iPhone as you are using to log into www.iCloud.com. Then make sure that your iPhone has iCloud notes enabled. To do that (once its connected to wifi) go into settings > Notes > default account > and then ensure that iCloud is selected. You may want to also disable the 'on my iPhone account' because those notes may not sync to the iCloud, depending on your settings.
Now you can head over to the iCloud website and from there you will see that your notes are all viewable as well as ready to update. If you delete a note from the iCloud website, it will also delete across all you other devices, so make sure you keep that in mind. Use this resource if you need to recover notes that were accidentally deleted.
You'll also find that Pages, Numbers, Keynote, and iCloud email are all accessible from the website if youre using a computer.
-Big_Tex