The Selective Service System has a page dedicated to this. The
following is their brief description of the draft procedure:
A lottery drawing - the first since 1942 - was held on
December 1, 1969, at Selective Service National Headquarters in
Washington, D.C. This event determined the order of call for
induction during calendar year 1970, that is, for registrants born
between January 1, 1944 and December 31, 1950. Reinstitution of the
lottery was a change from the oldest first method, which had been
the determining method for deciding order of call.
366 blue plastic capsules containing birth dates were placed
in a large glass jar and drawn by hand to assign order-of-call
numbers to all men within the 18-26 age range specified in Selective
Service law.
With radio, film and TV coverage, the capsules were drawn from
the jar, opened, and the dates inside posted in order. The first
capsule - drawn by Congressman Alexander Pirine (R-NY) of the House
Armed Services Committee - contained the date September 14, so all
men born on September 14 in any year between 1944 and 1950 were
assigned lottery number 1. The drawing continued until all days of
the year had been matched to lottery numbers.