You can make a calendar in Google Docs with a table, or with a Google template. Insert a 7x6 table into your document. Fill the first row with the days of the week, and the remaining cells with the dates for that month. If you want to use a pre-made template, go to the Calendars section of the Template Gallery.

On your computer, open a Google Doc. At the top left, click Insert Building blocks Calendar event draft. You can also type "@calendar event draft" in the doc and click Enter. To add people in the "Guests" field, type "@" and search your contacts, or type out email addresses.