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).

What are the winter solstice and the summer solstice?

In the Northern Hemisphere, between the equator and the Arctic Circle, the winter solstice indicates the beginning of winter and occurs when the sun rises and sets on the horizon farthest south for the year, and daylight length is at a minimum, ranging from 12 hours and 8 minutes at the equator, to no sunlight at all at the Arctic Circle. (In the Southern Hemisphere the summer stolsice occurs on this same day.)