All of us think, plan and work differently. A program that works well for a colleague might not work well for you simply because you learn and think in your own way. This is why it’s useful to research and try several different ways of compiling your checklist before deciding on a single system.
To use your checklist, simply work your way through it in order, dealing with the A priority tasks first, then the Bs, then the Cs, and so on. As you complete tasks, tick them off or strike them through.
You may find it easier to compile several checklists (covering personal, study, and workplace, for example). Try different approaches and use the best for your own situation.
But in you’re in an operational role, or if tasks are large or dependent on too many other people, then it may be better to focus on a longer-term checklist, and "chip away" at it day-by-day. Many people find it helpful to spend, say, 10 minutes at the end of the day, organizing tasks on their list for the next day.