What are the dates for the seasonal changes in 2013?

Spring - Begins March 20, 2013 (spring equinox) at 7:02 am EDT.
Summer - Begins June 21, 2013 (summer solstice) at 1:04 am EDT.
Fall - Begins September 22, 2013 (Autumnal equinox) at 4:44 pm EDT.
Winter - Begins December 21, 2013 (winter solstice) at 12:11 pm EST.

Source: Chase's Calendar of Events 2013, pp.614. 

What are the vernal equinox and autumnal equinox?

 In the Northern Hemisphere, spring begins on the vernal equinox (also called the spring equinox), when daylight length (the interval between sunrise and sunset) is the same everywhere in the world (approximately 12 hours and 8 minutes). (In the Southern Hemisphere the autumnal equinox occurs on this same day.)

In the Northern Hemisphere, autumn begins on the autumnal equinox, when daylight length is the same everywhere in the world, again approximately 12 hours and 8 minutes (In the Southern Hemisphere, the spring equinox occurs on this same day).