To level up the equipment, you will need to have the same equipment as the equipment you want to enhance.
Equipment can be obtained through summoning, see below for detailed instructions:

1. Click on the [Hero] at the bottom of the game screen.
2. Then click on the [Inventory] option
3. Select the equipment you want to level up
4. Click on the [Level Up] option

Also, if you apply the [Auto Level Up] mode (click on the [Hero] on the main page), you can enhance or synthesize the equipment at once.