After adding proper ingredients to the table you're able to start upgrading. As soon as you click the 'Upgrade' button all ingredients (the item itself and the items you're using to upgrade it) are being taken from your Inventory. Upgrades use the same alchemy slots as any other alchemy operations do and require some time to perform similar to other alchemy operations.
You can speed up upgrade process by adding catalyzers and assigning one of your allies to the 'Alchemist' position. It is also possible to use gems to complete the ugrade process instantly.
Please note that the items used to upgrade are taken from your inventory at the beginning of the process so if you've used an item which was equipped to one of your slots - it will be taken off. The resultin item will become available for equipment only when the upgrade will be finished.