Beam weapon damage falls off according to the factor (Range / Range_Modifier), capped by the maximum damage of the weapon of course. If you're unclear what the range modifier is, it is the value which is multiplied by the weapon damage to obtain the maximum range - for lasers this is the wavelength tech, for railguns this is the launch speed tech, for both of these the progression is in increments of 10,000 while for plasmas it is fixed at 10,000.

Consider a 15 cm laser (max 6 damage) with NUV wavelength (range modifier 30,000). At a range of 30,000 km or less, it will deal the full 6 damage. At a range of 60,000 km the damage will fall off to 3. At 90,000 km the damage is 2, and at the maximum range the damage is the minimum value of 1 (I don't remember how rounding works for the intermediate values).