There are several ways to aerify your field. Any of these methods are good because you are reducing the compaction of your field. By doing this, you allow the rootzone to be relieved of all the pressure that has been applied from hundreds of people on the field in the past year. With core aerification, you will need to have a plan for the cores that are being pulled. Some people harvest the cores, others topdress with sand and then drag the cores back into the surface with the sand.
Some people mow the cores back in with their reel mowers.
With the other two methods of aerification, you do not have the cores to deal with, so it is less time consuming to aerify that way. Also, after you aerify, you will need to topdress your field with sand. This allows the sand to fill the holes or slices and allows water, air and fertilizers get down to the rootzone. You want to maintain a sharp, crisp edge on your field and this is where edging plays its part. I am not suggesting that you edge your field daily, but you need to watch the grass and have a plan to edge the field all along during the summer.