My first thoughts were to do something like a "challenge mode", where you set goals for the new players and they try to achieve them as quickly as possible.
First few 'challenges':
1st to province with only X card in supply:
1) Market/chapel (teach trashing...prob best to start them out 5/2 though, unless you want to learn overtrashing too!)
2) Silver/gold : (Teach big money)
3) Village/smithy? (Teach counting total money in deck, plus light engine building practice - could be brutally slow though)
Engine/Deckbuilding:
"Draw your deck" goals with:
I'm sure there are more interesting 'tiny' boards, but if you were to play these 'games' in quick enough succession that people remembered the rough # of turns it took to complete each challenge, it might be a reasonable crash course. You'd probably want to add something much faster, too, to show that big money isn't the only way to play.