You roll your weapon skill to determine if you hit or not, then you roll damage and add your strength modifier. 

To determine mitigation you subtract armor for the area hit and the toughness bonus from whatever the damage was. 

So lets say I'm melee-ing a guy.  I roll a 26, which hits, so I reverse the numbers to determine which part of him I hit, in this case 62 hits the body.  I roll a 5 on my damage, and add my str modifier of 3, for a total of 8 damage.  But the guy is wearing something with armor 2 on his body, and has toughness 30.  So I subtract 2 for his armor and 3 more for toughness.  He takes 3 damage from my hit, (assuming no further penalties for the quality of his armor vs. the quality of my weapon)