See also the official documentation:
Help Center > Members Manual > Working with calendars

Adding a repeating calendar event

An example...

Click on "+Add Event"
(fill in "Event Name")

Make selections for the first occurrence of the Event in the "Date and Time" section.

In the "Repeats" section:

• Check the "Event Repeats" box
• Select "Monthly" in the "Repeats" dropdown menu (below the "Event Repeats" box)
• Select "2" in the "Repeat Every" dropdown menu
• Choose either: "Repeat by day of the week" or "Repeat by day of the month"
• (Make "Starts On" and "Ends" selections)
• The "Repeat Summary" will say either:
• Every 2 months on the <1st, 2nd, 3rd, 4th, or 5th> <name of Day of Week>
• Every 2 months on day <number of day of month>
  
  Important, finish setting up the event:

• Fill in "Event Information" section
• Set up Reminder notices in the "Reminders" section
• MOST IMPORTANT at the bottom of page:
  • Click on "+Add Event", or "+Add Event & Invite Group" to send out an immediate announcement.

Known Issues

October 20, 2019: there are still some features not available:

Groups.io currently doesn't recognize that there are 29 or 30 dates every year that are a 'fifth <day of the week>

Strategy: If you go to a last day of a month that has five and create the event there you can select:

Repeats: Monthly

Repeats Every: 1 months

Repeat by day of the week

Then the Repeat summary says "Monthly on the Fifth xxxday", and it means exactly that.

You could also set up a repeating event for the Fourth xxxday, but in months that have a fifth you'd have to manually delete the instance on the fourth.

It was also brought up that some events' date are calculated as being x days before or after another date.

e.g. Federal Election Day in the United States is the Tuesday following the first Monday in November in even years

     (1st Monday of November plus 1 day, repeats every 24 months)

(Some States also hold elections on that date every year, or every other but on odd years.)

https://beta.groups.io/g/main/message/17903 2018.08.06

Other options for a monthly reminder - see Member Notices (Monthly reminders and Group Guidelines.

October, 2020: Some changes to repeating events do not "take":

Some users have reported that certain changes to future events for a recurring event do not work. For example, event reminders continue to be sent after deleting future event reminders. 

See the Beta Group discussion topic: https://beta.groups.io/g/main/topic/74962529