I am a dwarf fighter with a +1 greataxe, and Dwarven Weapon Training (+2 damage).
For a 1[W] damage I assume I roll 1d12+3, but for a 2[W] attack do I roll 2d12 and add 6?
Any help on this would be awesome.
When you see [W] in a damage expression, it just means the weapon die as per the basic equipment description. For your character with the greataxe, that means 2[W] equals 2d12
All the bonuses add afterwards, they are not multiplied. Bonuses from feats and equipment are not included in the damage descriptions of powers, but how to add them is described elsewhere in the rules. For example, if you have the compendium look up "enhancement bonus" in the glossary.
Most powers, including Basic Melee attacks, will also add a stat bonus (Strength bonus by default for Basic Melee, and for most Fighter powers). So your damage with a 2[W] power is likely to be 2d12+7 or higher (it will be 2d12, +1, +2, +Strength mod)
From comments (Mooing Duck): There might be one or two exceptions to this general rule for damage bonuses. But you are safe in assuming that a bonus to weapon damage adds once (and not per die) unless you see the exception written for that specific bonus.
[W] means the damage die of the weapon including static bonuses. Static bonuses are magical enhancement bonuses on the weapon, any such damage boosters such as dragonshards, which are augmented to the weapon