How do you determine the critical hit damage done by a dagger? I'm a new player to D&D the board game, and don't have a campaign yet….
Anyway, I don't understand "19-20/x2" (as said on the weapons chart under critical)
(and yes, I have a Player's Handbook, I just don't understand that part).
The "19-20" part means that you threaten a critical if the number on the die is a 19 or 20. The "x2" part means that if you threaten and then successfully confirm a critical, you roll damage 2 times.
If only a multiplier is listed, it means that you only threaten a critical when you roll a 20 on the die, and, if confirmed, you roll damage the number of the multiplier times.
See http://www.d20srd.org/srd/equipment/weapons.htm#critical for more details - or just read the rulebook; If you don't familiarise yourself with the rules, you'll have to learn during the game... Which may or may not be a problem, depending on your group.