On December 1, 1969, the Selective Service System of the United States held a lottery to determine the order of draft (induction) into the U.S. Army for the Vietnam War.
The days of the year, represented by the numbers from 1 to 366 (including Leap Day), were written on slips of paper and the slips were placed in plastic capsules. The capsules were mixed in a shoebox and then dumped into a deep glass jar. Capsules were drawn from the jar one at a time.
The first day number drawn was 257 (September 14), so all registrants with that birthday were assigned lottery number 1. Men of draft age (those born between 1944 and 1950) whose birthday fell on the corresponding day of the year would all be drafted at the same time. The highest draft number called from the 1969 lottery was number 195 (September 24).
1969 draft lottery scatterplot. A scatterplot of the days of the year (horizontal axis) and their ranks (vertical axis) shows a noticeable absence of days in December with high ranks (later induction).
A secondary lottery was also held on the same day, to construct a random permutation of the 26 letters of the alphabet. For men born on a given day, the order of induction was determined by the rank of the first letters of their last, first, and middle names. 
The lottery was conducted again in 1970 (for those born in 1951), 1971 (1952) and 1972 (1953), although the 1972 lottery went unused as the draft itself was suspended in 1973. Lotteries were also conducted in 1973, 1974 and 1975 although the assigned numbers went unused.
More info here including newspaper reports and the full results of the 1969 lottery (I was born on May 26 and wouldn’t have been drafted had I been old enough.)