Each weapon has a listed damage range using the normal "min dash max" format. Missiles and Torpedoes have a single number for damage because the min and max damage are always the same for these weapons.
If the attack scores a hit, and if it is a weapon with a damage range (IE. 1 - 4 damage for the Laser) then the weapon does damage in proportion to how far above 50 it landed on the attack roll. Example, if the random roll came up with a 100, the maximum damage would be dealt for the weapon. If a 50 was required to hit and a 50 was rolled, the damage on the weapon would be the minimum number. If a 90 is required to hit and a 90 is rolled, the damage would be the minimum figure.
The damage range is mapped out evenly across the possible rolls to hit. If a hypothetical weapon had a min damage of 1 and a max damage of 2 and were 50% likely to hit, 0 - 50 would miss, 51 - 75 would do 1 damage, and 76 - 100 would be 2 damage. If the same weapon were damage 1 to 5 it would be 0 - 50 miss, 51 - 60 deals 1, 61 through 70 deals 2, etc.