Go to the Resources menu via the menu in the top right corner of your screen.
Select the jewel you wish to upgrade from your jewels "Inventory" and place it in the first crafting slot.
In this example I have placed one of my 48 Yellow jewels in to the first crafting slot.
Now add shards until you see the Result turn to Luminous (see below).
Note: If the result does not turn to Luminous you may not have enough Shards or Essence to complete the upgrade.
In this example I have added 30 shards to a Tier 1 Yellow which will create a Luminous Prime Yellow Jewel.
At this point you will see an Essence cost. In this example you can see that the crafting of this Luminous will cost 23 Essence.
If you are happy to spend the essence and shards, click on "Improve" to create the new Luminous jewel.
Please note that higher Tier jewels require more shards and essence to upgrade.
Finally click on your new Luminous jewel to return it to your Inventory.