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Get some ender pearls by killing endermans and blaze powder which is crafted from blaze rods which can be obtained from killing blaze in the Nether. Craft eye of ender using ender pearls and blaze powder. Right click with the eye of ender on the end portal frame. Activate all frames to activate the portal.
First of all: it's not called 'The Ender Dimension', it's called 'The End'. You can get there by finding a stronghold, then activating the portal there. When you jump through you will go to The End. (You activate the portal using 'Eyes of Ender', made using Ender pearls and Blaze powder.)
The Ender Dragon is a part of Minecraft, not a mod. You probably need to update Minecraft.
In Minecraft you must find a stronghold that holds an end portal. You will also need 9 ender eyes to activate the portal. Ener pearls drop form Enderman and you can craft the ender eyes from them.
The eye of ender hovers because it follows the ender and is magical!