Same Method as above just a little more in depth. In this video I will show you everything from the very beginning of what you need and how to get to every location, I also give you tips on how to kill the ender dragon fast and to destroy the obsidian towers without a bow and taking no damage.
** UPDATE **
You can now skip the the nether by resetting the Chest items in the alchemy section of the map. Grab your blaze powder from the the chest and make sure to hit the B when the guide comes up. Walk away and come back to open the chest again and you should be able to pick up 20 blaze powder.
If you have issues with the Nether Crystals, return to the menu, click on your world, options, and reset the end.
Thanks to @MathGuy42