Each weapon has its own range that is written right next to the weapon. The first value indicates the normal range of the weapon and the second value indicates the extended range. In the extended range, you can still hit the opponent, but you only deal half the damage. If an opponent is even further away, they cannot be hit with the weapon.

Example: Mark carries a short bow and shoots at an opponent 6 squares away. Since this is within the normal range of the short bow (80ft = 16 squares), he rolls a regular 1d6 and adds +3 for his Dexterity. Rolling a 4 he deals 7 damage. The next enemy notices his companion being shot and tries to move out of the range. He is now 20sq away. However, this is still within Markus' extended range and with his next shot he hits for half the damage. Rolling a 4 again, he deals 3 damage ((4+3)/2). 

Standing at an elevated position to the target increases the range by +2 sq. 

Keep in mind that measuring diagonally each square costs 1.5 sq range.