I don't understand what dice I'm supposed to roll or anything. Do I roll my damage dice? I've never actually played a tabletop RPG so this'll be my first, so I guess my confusion is understandable.
I guess you are confused because you dice twice for a hack'n'slash: 1) dice 2d6+STR so see if the attack works out at all, i.e. if you hit. 2) dice your characters damage dice, e.g. 1d10 for a fighter.
For further information read the core rulebook, watch some youtubed livestreams of people playing the game, and join a hangout game via the dungeon world tavern (that´s the name of a google+ group).
Don´t worry, playing DW can be learen in an hour or two.
The standard roll for Dungeon World is 2d6. When the system asks you to Roll+(a value), you roll 2d6 and add the relevant value. For example, when you are told to "roll+STR", you roll 2d6 and add your Strength Modifier.
For melee combat, the basic move is "Hack and Slash", which reads as follows:
When you attack an enemy in melee, roll+Str. ✴On a 10+, you deal your damage to the enemy and avoid their attack. At your option, you may choose to do +1d6 damage but expose yourself to the enemy’s attack. ✴On a 7–9, you deal your damage to the enemy and the enemy makes an attack against you.
So basically, you roll 2d6+Str. If you get a 10 or higher, you hit. If you get a 7-9, you hit, but the enemy hits you too. If you get a 6 or lower you miss, and something bad usually happens (the enemy hits you, you drop your weapon, etc.)
Note that the GM and monsters don't really take actions like players do. The GM makes "moves" but mostly only in response to the players' missing or rolling the partial success on a 7-9.