There are a variety of ways to keep track of your period but the most important thing is that you record the first day of your period. It may also be helpful to record how long your period lasts but most importantly will be the first day of your period (what doctors call date of your last menstrual period). You can use your own calendar (whether on paper or your computer), or you can use an app.
If you have an Apple phone, the period tracker is built into the health app. Otherwise, you may want to download an app such as Flo or Clue, but keep in mind that any information you put in this application is recorded also by the companies that provide this app service. If you are ever concerned at all about your privacy, you can use your own calendar and/or notebook.