Transmogrification has been a hit in WoW. It is still subject to many (too many, too) restrictions.
It can be difficult to find an adapted set and what is going with what. Of course, you can check different pages out, like http://transmogfashion.tumblr.com or such, but if you have a male dwarf and you see the set on a female blood-elf, you might get a bit surprised when you see the result (after grinding for months in different dungeons to get all the pieces of the set).
To help you on the way, there is an add-on (that you can download from Curse, of course) called Mogit. You can download it from here.
This very good and extremely easy to use add on let you see how different pieces look on you (when you loot them or have them in your bag), but it lets you browse every piece of clothes in the game and lets you see how it looks on your character.
When you start the add-on and check it out, all possibilities will be on. That means that you will see all the pieces of equipment that can be bought at vendor, got for reputation, got as a quest-reward, drop from dungeons and raids, PvP reward… everything. You can filter that out. No need for you to see how these nice Tyrannical shoulders will look on you if you never go PvP.
You can filter by color: If you want a certain tone of color, you can choose a color on a colored disk and get the equipment matching that color.
When you have found what you want to get, you can export the link of the equipment that you can paste in your browser and get it directly from WoWHead. Then you can see where and how to get this piece of equipment. If it is too difficult to get by, you can right-click on the equipment and select another one if available (there are, generally). All the pieces of equipment appearing on the right-click are those who have the same skin. So just pick up the one easiest to get.
If you like transmog, then this add-on is a must.
There is a little video- tutorial about using Mogit, here. It might help you out.
The sound is a bit weak and it can be a bit difficult to hear, but it is of great help anyway (but listen with earphones).