How can we efficiently use Trello for marketing campaigns?

What type of campaigns are you managing? I've seen a lot of content teams use Trello to manage content publishing schedule. Trello is flexible for a lot of use cases so really depends on what is it that you need to accomplish.

Create boards for each campaign and break down tasks into manageable cards. Use labels for categorizing tasks like content creation, design, SEO, etc. Utilize due dates to keep track of deadlines.