Gaijin Hunter wrote a really in depth guide on how damage is calculated.
The oversimplified result of damage is just: Damage = [Physical damage] + [Elemental Damage] * Overall Defense.
There is also things to take note of when attacking. Weapon power, motion value, and sharpness all play a part in the "Physical" calculations.
"Elemental" calculation is determined by "shown amount" / 10 x resistance.
Overall Defense is everything from the Monster's resistances, The type of quest (caravan, gathering hall, low rank, high rank, G) food bonus, etc.
The numbers you see on the weapons are very much "increased" than what you will actually do. In the example used on the guide (Shagara Charge Blade) has 648 damage and 230 dragon element, but attacking the Shagara's head deals a total of 28 damage once all calculations are done.