To add a new item to your subscription, you will go through the same process as when you placed your first subscription order as you'll just need to select "Subscribe & Save" instead of 'Add to Cart' when selecting the item you want to order.
It will still require you to go through the order process and enter your payment information the first time with a new item, but going forward it will auto-process and ship out monthly on the same date the order was placed initially unless you make changes to the frequency of the shipment once the first order has been fully processed.
Please keep in mind that first-time subscription items must be placed online by the customer. Customer Success agents are not able to place orders over the phone for first-time subscription items, but they can make adjustments to items that are already set to subscription if needed.