Planning is the first phase of any project, no matter how small. You wouldn't start a house without doing it, and you shouldn't start a software project.
Planning happens in a few stages: if this seems like a lot, don't worry - for small projects, many of these stages involve just a few minutes of your time. Just think of this as a checklist - remembering what you're supposed to do is important, even if some of the steps get skipped on purpose.
The first step involves a review of the project brief. Are there any questions left over? Have all the important roles been defined? Are critical dates listed? Is a budget defined, even if it's only approximate?
Don't forget the most important question: Is the project's purpose clear. Without a clear definition, you're doomed for failure.
Once everyone's happy with the project brief, everybody signs off on it and the project starts.
A project schedule means committing to delivery dates. Getting these dates on the table and committing to a budget up front is importat to make sure that everybody is on the same page.
Think of the Project Plan as a response to the Project Brief. It summarizes everything in it, and outlines how the projects goals are going to be achieved. It's a road map for the project.
Once everybody's agreed to a plan, we move on to the Execution phase.
Planning is more important than ever in software development, and it's happening less than it ever has. A project without a plan is a recipe for unhappiness.