Google Calendar is an easy, robust and free way to add a calendar of events to your site. You manage your events directly through Google's interface and the changes are automatically added to your calendar.
You will need to sign up for a Google Calendar account, if you don't already have one. You can do that here.
Once you get up and running with the calendar (adding events, what-nots and what-have-yous), you can add it to your site with these steps.
In the calendar list on the left, click the down-arrow next to the appropriate calendar (you can create more than one) and select the Calendar Settings option.
Go to the Share this Calendar tab and check the box to "Make this calendar public." Be sure to Save this change after you make it.
Then select the Calendar Details tab and go to the Embed this Calendar section.
Highlight and copy the provided embed code. This is what you'll use to add the calendar to your site. Note that, while you're here, you can also use the "Customize" link above the code to make changes to the look and size of the calendar.