They would determine the age of the site through multiple processes. There's a pretty good summarization (and in laymans terms) of the methods on
the NPSAEP website under the
ARCHEOLOGY FOR INTERPRETERS section. Another pretty good
source of information can be found on
encarta's website.
Basically, to determine an absolute date of a site that's less than 7,000 years old, you can always depend on radio carbon dating. This is
especially true when it comes to earthen pottery because of how it was made (partices of various organic matter were mixed in the clay to give it
different cooking properties when it was cooked in a kiln, stuff like grass, seeds, crop husks, etc., or, decorative items like shells, bones, etc).
Pottery is simply heated mud (clay), it's not melted (700-900 degrees doesn't melt rock) so the particles left over have a very precise radio carbon
signature that's basically from the day it was cooked.
Hope some of this was helpful to you.
I think it was an interesting find.