1) Start with the corp deck. Explain the starting setup, and the concept of actions. I usually say, "the corp gets four actions per turn, but the first must ALWAYS be to draw a card." The details of why this is not technically an action I save for later.
2) The first and most important thing is scoring agenda. It's what the game is all about. So I play corp turns, one after the other, just to place an agenda, advance it, takes bits etc. until it is scored. I say "When the corp has scored 7 agenda points this way, it wins the game."
3) So...what does the runner player do to stop this? I then explain that he too gets four actions but none are prescribed, and there is a new type of action, the Run. With a partially advanced corp agenda on the table, I demonstrate the effects of a run on R&D, HQ, and the SDF. I point out that if the runner scores 7 agenda points this way, she wins the game.
4) Then it's back to the corp. How do they prevent the runner from scoring their agenda from them? Now it's time for the concept of ICE, rezzing, and the full run sequence (approaching ice, rezzing or not, effect of subroutines).
5) So how does the runner get through this ice? Now it's time for icebreakers, MU restrictions, how to pump strengths and break subroutines, calculate bit costs etc. We talk about trashing programs and other ice effects like net, meat and brain damage. The concept of flatlining comes in here.
6) Finally I get to traces and tags, baselinks and increases to link.
I've found that this back and forth sequence makes it clear at each step WHY we are talking about the concepts we are talking about. Hope this helps.