To show the weather forecast in your calendar, go to settings, choose your location and select "Show weather based on my location". Note that there are countries where you won't see this option.
If you want to include special Google doodles, click on the "+" next to "Other Calendars", select "Browse Calendars" and add Google Holiday Logos, a slick calendar that shows a modified Google logo and the details about specific holidays. You can also add "Phases of the Moon" calendar, to see the date when the moon phase changes.
