May First is also International Workers Day, a holiday first popularized by the Soviet Union. While it has lost many of its communist associations, it still is vigorously celebrated in former Soviet-bloc countries and other places in Europe. You can expect worker's groups and unions to be active today; major strikes are sometimes scheduled for May Day.
Since May Day corresponds with the peak of the flower season, flower shows and festivals are common. The ancient Minoans are believed to have celebrated one of their two "New Year" celebrations about this time - the other was in October.
One very common commemoration is the making of a May wreath which is hung on doorways, balconies, in chapels, and many other places. Keep an eye out for them.