You can use the function do_shortcode in your template to output the content generated by the shortcode that My Calendar provides for listing events.
For an example, to show a list of upcoming events use something like:
<?php echo do_shortcode('[my_calendar_upcoming before="3" after="3" type="event" fallback="No events coming up!" category="General" template="{title} {date}" order="asc" skip="0"]'); ?>
Take note of the use of single quotes for the function and double quotes for the shortcode attributes.