I used to be a game demo person for Wizards of the Coast. You know, that company that makes Magic: The Gathering. I would go to stores and conventions and teach people how to play all the games they made. I was pretty good actually. I could teach people how to play games quick and get them interested. A lot of my demos turned into sales at conventions while I would see other game demo people struggling to explain the same games to them. Often, I was tasked with teaching the more obscure games because of how good I was at teaching games.
Anyway, what I learned is to keep it simple. Hold back and don't teach everything. This goes for Magic or any other game whether it be a board or card game.
So, for Dominion, the trick is to hold back mechanics. My recommendation is to hold back showing Moat and Witch at first. I would also recommend holding back Gardens since there are the regular VP cards already present. Yes, the first game has Moat in it. I recommend swapping it out.
For game 2, keep 5 cards from the previous game and introduce 5 new cards. Why? The 5 cards are familiar. This makes it quicker to learn the 5 new cards. Whereas is you go with 10 all new cards, it is almost like learning the game all over again. Also, this makes it easier for new players to memorize the 5 cards from the previous game. Essentially, this speeds up the learning curve and makes it both quicker and easier to learn the game.
For game 3, mix things up. If you have been doing engine games, go for a slog. If your first two games lend more big money, try to make it more of an engine thing. Also, game 3 would be a good time to introduce Witch and Moat or Gardens. Or even all 3.
Seaside is a fairly straightforward for the most part. I tend to introduce cards from Seaside and Intrigue at the same time. My recommendation though is not to introduce both the mat cards and durations at the same time. Introduce one new concept at a time.
A couple of months later and many games, introduce Prosperity. Just skip Alchemy for now. Why wait on Prosperity? Because by waiting to show off Colonies and expensive cards, there is more of a WOW factor and that's a good thing. I know you are dying to show off these cards, but be patient. Again, introduce just 5 new cards at a time.
After Prosperity, it is up to you where to go. I would save DA and Alchemy for much later. While Adventures seems very complex, I think the WOW factor of Events may make it worth it to teach it to them before DA. You might want to show off Guilds or Hinterlands first though. When teaching Adventures just remember to hold back. Introduce Events with the new Durations but hold off tokens and Reserve cards for another game. Next game show off the Reserve cards.
Anyway, good luck to you in teaching Dominion. I hope this brief guide proves valuable to those wanting to get people into Dominion or who aren't sure how to go about introducing new expansion to their play group.