1. Make sure the supplier has an Email set (Settings > Kitchen Settings > Suppliers); only suppliers with an email get a Send Email button.
2. Open the Inventory Shopping List for the date range you are buying for.
3. Click Send Email in the supplier's header. An Email Preview opens with the generated message.
4. Click Send Email in the preview to send it; the button turns orange and reads Resend Email afterwards.

To email everyone at once click Send All Supplier Emails at the top, review the list of suppliers and addresses in the pop-up and click Send All Emails; each row shows Pending / Sending... / Sent / Failed. Only ingredients whose Total Needed is greater than zero are included; if nothing is needed you get "No ingredients needed for this supplier."