Memorial Day has always been in May, although the date has changed over time. It began as a holiday to commemorate those who had died in the Civil War, which ended in 1865. There were several such ceremonies in the year after the war, but the “official” beginning (as declared by Congress and President Lyndon B. Johnson in 1966) was one in Waterloo, New York on May 5, 1866, which honored local veterans who had died in the Civil War.
Two years later, Major General John A. Logan of the Grand Army of the Republic announced what was originally known as Decoration Day.
The 30th day of May, 1868, is designated for the purpose of strewing with flowers, or other decorating the graves of comrades who died in defense of their country during the late rebellion, and whose bodies now lie in almost every city, village and hamlet churchyard in the land. In this observance no form of ceremony is prescribed, but Posts and comrades will, in their own way, arrange such fitting services and testimonials of respect as circumstances may permit.
The first (official) Decoration Day ceremony was held at Arlington National Cemetery.
While the ceremony was originally intended to honor only those who died in the Civil War, after World War I it was changed to honor all who had died in US wars. The date remained May 30 until 1971, when the Uniform Holidays Act changed it to be the last Monday in May.
One interesting note: Frank Woodruff Buckles was honored in a special ceremony this weekend. At age 107, he is the last known US veteran of World War I (having lied about his age in order to enlist in the Army). You can read more about his story here, and more about the history of Memorial Day here.