For the first dimension, the Blind Oasis Dimension, you will need to get Black Quartz Ore from the nether and use Black Quartz Blocks for the portal frame, similar to the nether portal.  However, to light it you cannot use a flint and steel; you will need a Blind Oasis Activator crafted with 2 pieces of Onyx and 1 Black Quartz Block in the middle. Mobs will be ready to welcome you into the dark so come prepared.

You will need to collect Blindonite Ore from the Blind Oasis Dimension to advance to the next dimension, the Vaeryn Dimension.  Again, you will need Blindonite Blocks for the frame but you must use a Vaeryn Activator to light it. This is crafted using 2 Blindonite and 1 Blindonite Block in the middle. This dimension is much more satisfying than the other - a bright blue sky, light trees.  But beware of the mobs that guard it...