The portal is the gateway into the mod's deeper dimension, and it is built from blocks found in the Deep Dark rather than from obsidian. You will need to gather materials from an Ancient City before you can construct one.
Building the Frame
Collect 
Heart of the Deep items, which drop from hostile mobs in the Deep Dark such as the Shattered and the Stalker. You also need 
Gloomslate and its variants, which you mine from the dark stone around Ancient Cities. Arrange the frame in the same shape as a Nether portal, using the appropriate portal frame blocks from the mod. The exact block you place in the frame corners matters, so check the in-game recipe book or JEI/REI for the portal frame block before you commit.
Lighting It
Once the frame is complete, use the item the mod provides for ignition on the inside of the frame. If nothing happens, your frame shape is wrong or a block is missing. A correctly lit portal fills with a swirling dark surface. Step through and you arrive in the mod's dimension.
If It Will Not Light
Break and replace the bottom row, confirm every frame block is the correct type, and make sure no blocks are obstructing the interior. Portals also fail if the frame is not the right size, so rebuild it to the standard portal dimensions.