This part of outfitting is the most fun! So many combinations are possible that it is hard to say what is right and what is wrong. However as a rule you can keep the following in mind:

Colours
Try to use no more than two or three colours in an outfit. That way it will seem like the pieces really belong together.  When using the Dressing Room preview feature (ctrl+ left mouseclick), check all possible colours. You might be surprised how a different colour can change the appearance of a dull item into something special.

Hues
Dyes give different hues depending on the item’s basecolour. Try to use a neighbouring colour if results do not match. Examples of neighbouring colours are red/crimson, rust/orange/sienna, violet/indigo, turquoise/seablue etc.

Dyeable/Non-dyeable area
Each item has a dyeable and non-dyeable area. Try to match the undyeable part of an item with the dyeable part of another item. For example: if there is an unchangeable green area in a cloack and an unchangeable brown area in a chest, dye the chest green and the cloak brown. They suddenly seem like matching items.
Some unique items, most pre-order items and Helegrod raid armour cannot be dyed.

Styles
There are typical man, elves, dwarves and hobbit styles. Mix and match styles to suit your fancy! I don’t think there really are any rules regarding what works and what doesn’t. If you want to stay on the safe side you can work within one type of style, but it is thinking outside of the box and doing things a little different that will give the most amazing results. Let your taste guide you.

Wardrobe usage
Use the wardrobe for some standard base items that you can use often and with anything. Some good gloves, a number of boots, shoulders and some cloaks. Dye these items in several colours in order to use them in all your outfits.
You can keep dresses and hauberks in your wardrobe too, but these items are used much less frequently and usually just taking up space, and believe me, serious outfitting gobbles up all of your vault, shared, chest and alt space. Keep the original items and delete the wardrobe copy when you get tired of it.
Keep some wardrobe slots open and dedicated to items that you are only using for a limited time, like festival items.

Inspiration
Check what everyone around you is wearing. If you see something you like, inspect the player to find out what it is.
Take a look at the Turbine forum thread to find out what other people have come up with.
Use the links in the side-bar of this blog to check other outfit blogs.
Use the colours of your favorite horse to design a riding outfit.
Make outfits for different weather conditions or activities and slot them in different panels so you can switch as you enter a different region.

Above all: have fun!