The client side of things will look like this:
Step 1: client will receive an email from Microsoft notifying them of a shared item
Step 2: they can click Open and it will bring them to a page where they need to verify the email address that the shared document was sent to:
Step 3: after they enter their email address, a verification code email will be sent to them from Microsoft
Step 4: after they enter the code, they will be able to access the shared document. if they need to upload a document back to you, they will click Upload and select the file or folder to be shared with you.
Note that you will not receive a notification if they upload.