How do you encourage people to adopt Trello and make sure people know how to use it?

Tell them all the cool kids are doing it! But seriously, take the time to share with them how well it works for you first, and then see how that might answer some of their needs they may be hesitant to bring to Trello. Key features that I like to share with others is its easy-to-use user interface for scheduling tasks and visual organization. You also can't beat free, which is a huge win for a lot of people. Hope that helps!

On top of what Corey has written. The Watch feature is great as it means if the card is managed by someone else then the user will get an email if the card was changed/moved with a link back to the board and a quick note on what happened to the card.