I usually take the starters from FOTR and we play with them hands up after giving them the basics of the game. You should keep the back of a rulebook in front of them so they can see the phases of the turn as you play the game. By the end of the first game they have a good enough grasp on it to play normally.
The reason for using FOTR is because, at its core, it is the least complicated of the sets to play. You do not need to worry about describing site control/liberation, threats, resistance, etc. and the sites numbers are all set out to be played in order.
And for the comment on letting them win, I do the same thing that was done with me when I started to get into CCGs (SWCCG way back around Dagobah): If they make a mistake that is detrimental to them I point it out the first time and explain why that is not the best move. Then if it happens again in the future I hand them their backside. Ther person usually learns real fast to not do that again after getting it handed to them. It is much more satisfying IMO for a newer player to get a win after playing well against someone that they know is better than she/he. I still remember the first time I beat our resident "pro" Jared in SWCCG years ago. Man I could never beat that guy for the longest time, but #$&*@! it felt GREAT when it happened the first time.