What is the best way to explain the process of combat in Dungeons and Dragons?

I've found that explaining it is difficult, to say the least. The best way to help someone learn the combat system really is to just sit them down with a pre-made character and do it. You can simplify it by running a monster's turn first and making sure to explain everything as you're doing it. Then, when your PC's turn comes up, ask him what he wants to do and explain to him how to do it. (The following example assumes your PC is familiar with dice abbreviations and terms like "Armor Class.") DM: "Okay, the goblin takes a swipe at you with his handaxe. He rolls 1d20 and comes up with 18. He then subtracts -1 for his Strength penalty, which modifies his roll to 17. I compare that to your Armor Class - 15 - and his stroke lands. The goblin then rolls 1d4 for damage and subtracts -1 for being weak; the roll is 3, so he deals 2 points of damage to you. Your turn." PC: "Ouch! He's not getting away with that. I want to slice him open with my longsWord!" DM: "Okay. Make me an attack roll: that's 1d20, plus your Strength modifier, plus any other modifiers you might have like a masterwork weapon or the Weapon Focus feat." [For clarity's sake, I always total this stuff up beforehand, so the newbie PC only has to know "roll 1d20+3" or whatever.] PC: (rolls) "20! Is that good?" DM: "Not for the goblin. That's a critical hit, which deals double damage. Roll 1d8 plus your Strength modifier for it, then multiply that by two." PC: "Woo! Okay; I rolled a 7. My Strength modifier is +2, so that's 9; doubled to 18. What happens to the goblin?" DM: "Your stroke slices clean through his abdomen, separating him into two halves. His eyes filled with disbelief, he looks up at you as his torso falls to the ground. His legs sway for a moment, then fall as well." Upgrade the process as you go, adding the more complex maneuvers like tripping, bull rushing, and (Gods help you both) grappling.