This is the fundamental question that must be answered before any meaningful progress can be made toward establishing or refining a process. According to Merriam-Webster, process is "a series of actions or operations conducing to an end." A well-defined process within your organization allows easy oversight by stakeholders and seamless integration of contributors. Further, contributors have easy access to all required resources and assets to operate in the most efficient and effective way possible.
Ultimately, a well-executed process saves time and money. It eliminates unnecessary headaches and makes an organization look better to its clients. It allows contributors to interchange with less mess, which, you guessed it, saves time and money. It allows stakeholders to have a better view of an operation—from a top-level, macro view, to a detailed task view—with ease.
Establishing and refining a process is difficult. Keeping team members actively participating is more difficult still. Further, there's no single tool or one-size-fits-all solution for every team. However, it's easy to take small steps to improve. The first step is simply to want to, which, surprisingly, isn't a given.
The next step is to determine the pain points. Everybody loves a gripe, here's where it can be used for good. Is Jill tired of the confusion that comes when handing off tasks to her project managers? Is Hans setting up each project differently? Is everybody pulling their hair out when trying to onboard freelancers? Take note of common pain points, and determine which, if any technical solution might fit your requirements. Try different solutions when they're available to see which works best for your team.
Unfortunately, the latest and greatest software alone will not achieve a better process. In fact, it can often lead to a worse one. From my experience, the three keys to maintaining a process (because all good things come in threes), are: To establish a centralized, organized, up-to-date information source, an organization or a team-wide 'wiki'; to bucket information in such a way that an outsider could enter your system (theoretically) and easily find what they're looking for; and finally, most importantly, to get team buy-in—to follow and help refine the process. Without the third point, all the others are utterly useless.
You don't need to solve every problem in one day. Process takes time to establish and should constantly evolve. New tools will become available. Team members will come and go. Having a good process in place will help ease these transitions and keep you and your organization moving forward.