If the customer only has one subscription and you just want to upgrade that to a new package, you can do it through the "packages" tab when viewing the customer in the UI.
If the customer wants to move a website between 2 packages they are subscribed to, they can't (yet) do this directly. The method would be to move the website to your parent organisation from the "..." menu on the customer management view, website tab. Then on the main website listing, go to "..." then "transfer to customer" and choose the customer and the destination package there.
