Recording your running progress is an excellent way to both track your running progress and improvements, and to give you some kind of measurable variable that helps you understand how close or far you are from your goals. Plus, writing things down has been proven to be beneficial in keeping us accountable and helping us maintain our focus on what is important and what we want to achieve.
Start out by writing down your running goals. Again, writing them down and having them printed on paper makes them more "real". They are not just stirring around in your head for you to change or give up on without having to physically erase it from a piece of paper or tell others. Writing it down solidifies it, and it makes it more likely that you will work to achieve it.
Then you will want to create smaller, individual goals along the way that will help you attain your overall goal. This allows for your running improvements to be made in a timely way that you can prepare yourself for, mentally. The number of times you record and track your progress depends on what and how lofty your "big" goal is. For instance, if you are starting out having never ran a race before and your big goal is to run a marathon, then you will definitely need to set some smaller goals for yourself along the way that will help you eventually get to the place that you can run a marathon. That might mean signing up for a few 5ks or 10ks, a half marathon, and definitely scheduling some significant long runs and timed runs throughout your training.
I would start out by making two or three goals each month, but then after a month or so, if you decide you need to be making progress and improvements to your running faster in a shorter period of time, try making weekly goals. Not only will these small goals help you reach your big goal, but once your "big goal" has been reached, you can look back at your records and progress and see where you might need to focus on in the future to even MORE improve yourself and reach your goals.