In the past when introducing a new player to roleplaying games I have found they understand it much quicker if I handle the mechanics of the game, and let them experience the story and play without having to pay attention to the background. I also find that this makes for more immersive experiences for the players, at the cost of some control and agency. Every introduction previously however, has been running Dungeons and Dragons in the background.
I learned this back in AD&D from my first DM, and started doing it without really paying attention to it to all players. Of course, in AD&D, I could get pretty far with just knowing to-hit and THAC0, and players seldom needed to know statistical information other than "I'm good at hitting things" or "That thing is really big, and fighting it would probably be a bad idea." There was relatively little weird abstractions. When we moved the 3rd edition, we found it was easier for experienced players to keep track of the larger amount of information, but I could still easily make a character with a new player and just ask them what they were doing when their turn came around, making all dice rolls for them in the background behind the DM screen. I introduced two new people like that, and eventually they picked up enough of the chatter of the rest of the group and were able to start keeping track of their own information.
I'm now about to start running a Dresden Files campaign with a player who is new to any kind of roleplaying game. In FATE, the difference between an attack and a maneuver in particular is narratively very similar, but mechanically very different. Heck, some blocks could sound very like attacks. How do I "hide the numbers" in FATE game? If the player says that he wants to punch someone and land them on their backside, is that an attack, a maneuver, or a block against movement? I think I can hide damage easily ("He swings a sword at you. You jump back, but find yourself with a gash across your leg.") but I'm just not sure how to interpret the attacks.
Bonus points- the player wants to play a spellcaster. In D&D this would be no problem- the vancian system seems very understandable in my experience. I have no idea how to hide this in Dresden, since there are some very important mechanical decisions that have to be made when casting a spell.