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The Craft:
The apprentice tailor makes Rough Cloth Armour, Padded Armour, Heavy Cloth and Heavy Padded Armour for level 7-12 characters from light boiled hides.  You will need to boil these with Forestry skills or purchase boiled light leather from a Forester.  

The Hunt:
Gathering light hides as you begin your adventures in Middle Earth is simple. Many of the introductory quests require you to kill wolves, boars, lynxs, bears and bats. Light hides drop from all of these creatures. Hide drops are random so you will need to kill a fair number of beasts to advance in tailoring.  In many cases your beginning quests will require you to kill some of these useful creatures.  Most areas also have dens or other concentrations of creatures so that you can gain both combat xp and hide.
 
Work Orders for Hide
If you have time and money, you can pay the Hobbit lads in Overhill (Overhill Yards 27.7 S, 70.4W) in the Shire to gather Hide for you.  They will deliver apparently random configurations of hide.  For instance, my work order for Sturdy Hide gave me 5 units of Pristine Hide and 1 unit of Sturdy Hide.  A second order resulted in 1 Pristine Hide, 3 Sturdy Hide, 2 Drake Hide.  I was unable to pick up the Drake Hide, getting the infamous nasty-gram message “You cannot take that!” (Bugged this.)  You can only have one active work order at a time.
Place order with Tanner Bruce (Purchase it, right click on order in your inventory to activate, then talk to Tanner Bruce again to accept the quest and actually place the order).  You will see noted near the quest log how much time you have remaining till your order is ready.  It takes 40 hours for your order to be processed by the Hobbits. The timer begins when your order is placed and counts down even if you are not logged in. 
A check box and direction to talk to Skinner Grubb appears when your order is complete.
Pick up the key to collect the order from Skinner Grubb nearby, then right click on labeled Hides boxes to collect hides.
Pricing:
Light Hides 10 Silver per order
Medium Hides 20 Silver per order
Sturdy Hides 30 Silver per order
Note: this area is a great place to level up on your Tier 1 Forestry skills.  There is an abundance of Rowan wood spawns in the area to the west of the Overhill Yards, also bears, boars and the occasional wolf for Light Hides.  There are also spawns of copper, tin and various berries, vegetables and honey with the occasional spawn of Woad and Yarrow.  Overhill also has a grocer, two workbenches, a Novice Woodworker npc and a Grocer for your Wax and other needs.  Also, there is a handy Mailbox.

Cloth:
You will need to purchase cloth and thread from a Novice Tailor npc.  Apprentice level recipes call for Rough Cloth.
Price: A Bolt of Rough Cloth is 1 Silver, 60 Copper for each Bolt
          A Stack of 50 Rough Cloth Bolts is 80 Silver.

How to get recipes:
A basic set of recipes is granted to you as soon as you choose a craft set with the Mistress of Apprentices.
Brigands, Goblins and Dourhand Dwarves in the beginner areas can be a source of looted recipes, which often give more crafting tier points and enhanced stats to your armour. There are no recipes for purchase at the Apprentice level.
Another source of Looted Recipes is the Auction House.  Here you can find and bid on items you need.  Auction Houses are in Michael Delving in the Shire and in the Town Hall in Bree, in Thorins Halls (to the right and to the left as you enter the halls) and in Rivendell near the Last Homely House.

Tailor Advancement and Training:
Once you have gained your first 200 points of crafting experience, you will be offered a tailoring quest by the Novice tailor npc nearby.  A ring will appear over his head.  Right click on him and select the quest “The Thickest of Skins Part 1”.
The Thickest of Skins Part 1
Your novice tailor will say this:   “Tailoring is not an easy discipline to learn…, but if you can master its many complexities, you will be a great asset to those in need.  Carver Greenlake, a young tailor of some skill, might be able to assist you with the development of some basic techniques.  Look for him at Thornley’s work site, north of the town of Bree. Beyond that I really cannot say. “

Travel north along the Greenway outside of Bree to Thornley’s work site. 

Talk to Carver Greenlake (26.4 S, 53.7W).  Reward:  Craft Tailor Complete Proficiency Tier 1

Carver’s dialogue foreshadows the next level Tailor’s quest.

Once you have completed this quest, Journeyman level recipes will be available to you.

Mastery Options in recipes:

You need to master each tier of crafting (beyond the initial 200 points) before you are able to use mastery option ingredients in your recipes.  When the yellow mastery bar is filled in, you will hear a bell tone and an informational box will pop up telling you that you can now use the mastery options and ingredients in your recipes.
Using a mastery option ingredient gives an increase in Armour Value, and an enhancement to the stats of an item such as increased Power, Agility, Fate, Vitality, or Might.
In my opinion, adding mastery option ingredients to skill based recipes gives significant added value, but it adds little to the already enhanced statistics of looted recipes.