The following is adapted from by book Trello Dojo, all about getting the most out of the awesome organize-anything service Trello.
I obviously am a fan of Trello, and can't imagine anybody finding it difficult to use or confusing. However, I do occasionally run across people who, for various reasons are unwilling to give Trello a try or spend a few minutes with it and give up. I've had a few readers share similar stories- they personally thought Trello was the bee's knees, but their customer wouldn't be bothered.
My first solution, obviously is to tell them about this book. But for work projects, I do have another solution. Instead of asking the other party to participate in the board directly, simply set up a weekly status call using Join.Me. This simple app requires no download or login for the other party- they simply go to the website and see your screen. I've found a short (15-30 minute) weekly call to go over "what's happened, what's happening next, and what's being held up" is a terrific practice for managing projects.
While on the call, pull up your project board, and discuss the project (NOT the board). Be sure it's updated, add and move cards as needed, but don't mention Trello at all unless they ask. Best case your reluctant Trello-er will love what they see and will want to join in, at which point you can simply invite them to the board. Worst case, they still don't care about Trello, but you're organized and gain their confidence.
While it may not work in every situation, this can be a great way to wean projects into Trello without hitting people over the head with it.