For the current tutorial I have collated information in the comments, I believe this may be the last iteration on the X1, I have also left up the previous methods if they are applicable.
You can now load up the tutorial, dismiss the original tutorial messages and then head straight forward, head past the beacon towards the sign with the wings on it, below this is a chest with 10 leather in it, grab that, shut the chest and leave the immediate area, then head back and the leather should have respawned, so grab it again, this will give you 20 pieces of leather in total...we need 24, so repeat the trick and you should have 30 pieces.
Thanks to xPut Name Herex
With the latest update, chests respawn the materials in them when you re-enter a tutorial area. So you can go and grab those leather in the wings area, turn around and leave, then come back and grab the batch of leather again until you have enough. Just make sure to dismiss or complete the "do you want to learn how to do this?" prompt, as the game won't refresh the chest contents when it thinks it is mid-tutorial already.
Head back towards the beacon and stop at the chest with the banners and in there should be your Dye, pick any colour you wish. Then turn right and head down the steps where you should find the crafting table. Craft the four pieces or Leather Armour required, Helmet, Shirt, Leggings and Boots. Don't wear any of the pieces, keep them in your inventory.
The recent updates have added a menu for dying, explained below by OptimalShadez
The seems now that in order to dye your leather armor you need to open your crafting menu. Press LT and it give you a new menu to dye armor.
One final piece of advice from SpeedBumpVDrop
I'd like to point out that dying it with the Cauldron won't work.
Hope this helps, let me know if any further information would be useful.
TU 46 Method
TU 22 Method