Select Calendar from the Google Embeds section in the Insert menu.
After inserting it you can change the display to week, month or agenda.
Note that the calendar must be shared publicly in order for it to appear for everyone. See the instructions.
You can insert calendars that have been shared with you. In the insert menu scroll down to 'Other Calendars'.
See the calendar settings image below.
To maintain calendar colors don't use the Calendar tool from the insert menu but use Google Calendar's embed code generator to make the color-coding you want, and use the URL it generates as an Embed URL in your site.