klaymen: If the damage range is, say, 3d4 (broadsword) and you roll 7 in total, you do 7 damage (excluding enemy's damage resistance, character's strength bonus, etc.).
But if he damage range is 3d4+3, then you deal 7+3=10 damage.
Attack increases your hit chance, it doesn't affect the damage.
It is probable that a character's strength and skills (and maybe also level) will give a bonus to the damage. This roll merely determines the role of the weapon itself in dealing damage, but various character attributes and skills will also factor into the damage. I don't know the exact formula. Basically, giving a badass sword to your weak, unskilled wizard will result in dealing less damage than giving it to your strong, skilled knight.
It's also important to note that by using "dice" in this way, the probability of certain damage rolls can be weighted. For example, 2d6 will give between 2 and 12 damage, but not all of those are equally likely; since there are two dice, the most likely result is 7. However, a 1d10 weapon will give between 1 and 10 damage with each value being equally likely. If you are curious about how these probabilities work I'm sure there are many resources on the web telling the probabilities for various dice combinations.
It is a bit weird that this is never covered in the game manual, but these dice systems were popularized by Dungeons and Dragons to such a degree that I guess the game designers felt they didn't need to bother explaining it, because they thought everyone would already know.