Just remember:
All attacks are actually powers.
Some powers use Magical Implements to channel the damage/effect/etc while other powers use Weapons to channel the damage/effect/etc.
So, not EVERYTHING you do with a Longsword will use your Strength modifier for damage.
Basic Melee and Basic Ranged attacks are both powers. They both use the Weapon keyword for Accessory. Accessory is the keyword used to describe what object/accessory is used to channel the power. In 4e and the PHB so far, this is ALWAYS Weapon or Implement (at least for attack powers).
If you use a weapon with a power which says "Weapon" as the accessory keyword near the top of the power (don't confuse it with "Weapon weapon" which is actually a range), then this means that you get +hit with that power for anything related to that weapon... such as being proficient, feats, magical bonuses on the weapon, etc in addition to whatever Ability Modifier is listed ON THE POWER.
For damage, however, you pretty much use the same thing except you don't add the proficiency bonus.
An example?
A paladin is using a power which requires a Weapon to activate or use the power through.
Attack: Charisma +1 vs. AC
Hit: 1[W] + Strength Modifier radiant damage.
The paladin is using a magical Longsword +2.
ToHit:
+3 (prof with longsword)
+2 (+2 magic on the longsword)
+4 (for having an 18 or 19 Charisma and the power saying Charisma ... Something)
+1 (for the power saying Something +1 vs Something)
+1 (maybe he has a feat which grants him +1 to hit with heavy blades)
+1 (maybe he is under the effect of a teammate power which granted him +1 bonus on next attack roll)
+2 (he is flanking the target with a teammate which grants both of them combat advantage against the target)
-2 (concealment.... maybe you are fighting in low light or your target is in a cloud of mist/fog)
ToDmg:
1d8 (for the 1[W])
+3 (for having 16 Strength and it saying Something + Strength Modifier ... Something)
+2 (for the +2 on the magical longsword)
+1 (for him using it 2handed and it being a versatile weapon)
+2 (for some power from a teammate buff which gave him +2 to next damage roll)
+1 (for some feat which grants +1 damage to all 2h attacks or heavy blade attacks)
That should be a good start.