Building a project management tool like Trello without coding can be achieved using Bubble's no-code development platform. The process involves registering for a free account, completing introductory lessons to get familiar with common features, and then designing the product and building its underlying logic step by step. This guide will walk you through the steps of creating a new board, displaying a list of boards, sending data between pages, creating lists within a board, displaying tasks within a list, moving cards between lists, editing task content, and deleting tasks. With Bubble's free plan, users can build their product without any additional costs, and paid plans start at $25 per month to host the app on a custom domain. Additionally, templates and plugins are available for purchase, offering an easy way to build a Trello clone or other products without coding.