I have a very limited understanding of D&D concepts. How does weapon damage work in Baldur's gate?
Baldur's gate I & II use a modified AD&D 2nd edition, if I'm not mistaken.
The damage itself is expressed in dice, so e.g. 1D6 means you throw one six-sided die and count the sum of it. 2D8 means you throw two eight-sided dice and count the sum of the two dice. The damage gets subtracted from the hitpoints of your enemy.
Armor class (AC) defines the probability of getting hit. The attacker throws a D20 and if the value is lower than your AC you are hit, else the attacker misses. Certain bonuses apply to attacker and defender. You have to pay attention to your THAC0, which tells you what you have to throw to hit an enemy with an AC of 0.
Damage type also matters with certain armors having more or less protection vs certain types or are immune to some types of damage outright. This will normally be listed in the weapon description. Extra armor penalties/bonuses are listed in the character sheet near the bottom, or in the armor's description if you're playing in one of the Enhanced Edition games.
Here are some details. To damage, you must hit. To hit, you must understand THAC0 (To Hit Armor Class 0).
THAC0 is a value defined by your class (fighters have a lower THAC0 than mages).
When you attack, you throw a d20 and you subtract the value from your THAC0 to find the minimum AC value you hit.
Example: my fighter has a THAC0 of 16. If I throw a 16 on my d20, I would hit anything from AC 0 going up (remember, in AD&D 2nd Edition the lower the AC the better).
If I roll a 20, then I could hit an AC of -4.
After this, the damages work as answered in Fabian's post, with dice and strength modifiers. Also, some magic weapons have damage and THAC0 bonuses.
Damage is expressed in terms of thrown dice.
Formula for attacking:
A d20 die is thrown, and the value must be greater than or equal to the attacker's attack roll value. The roll auto fails on 1, and criticals on 20. Let's say, for example, I'm the Slayer, and I have a THAC0 of 1; I attack a creature with an armour class of -10; My attack roll would now be 11 (50% chance to hit).