When did the Selective Service System come into being and when did the Draft begin and end?
From this point, you are on your own.
The short answer is that the current Selective Service system was set up for the First World War and is still in place (with various changes and amendments over time). There has been no conscription since 1972, but the system remains available if needed.
There were, of course, drafts handled prior to WWI, especially for the Civil War. Those were done on a more ad-hoc basis.