You are
an obsidian (or the nether portal created with it)
I'm purple and small,
an obsidian is a deep purple (and also black) block. A nether portal can be created by a bunch of obsidians.
not hard to make at all.
Obsidian is formed when flowing water hits a lava source block, and can be found naturally where water from a spring or lake has flowed over a nearby lava pool. A Nether portal is absurdly easy to create, if you have enough obsidian to do it
I take you to new places,
Where you will see some new faces.
I'm part of the world, yet take you away,
When you step through me, you see mostly grey.
You must walk through me to complete the game,
Obsidian can be used to create a nether portal frame. Obsidian can be created when a Nether portal is spawned in the Nether or the overworld. This portal can then be mined, providing another way of obtaining obsidian renewably. When a player enters the End, a platform of 25 obsidian blocks is generated for the player to spawn on. This platform can then be mined, and will be regenerated when the player reenters The End. Solid pillars of obsidian can also be found on the surface which will regenerate when the ender dragon is respawned. Obsidian also generates as a part of end cities.
And when you see me, you'll know my name.
That's one of the ways you "see" things in the game - by hovering the mouse cursor above it. Also... Ob-"see"-dian? xD
Font of the answer:
http://minecraft.gamepedia.com/Obsidian