Sometimes the dataset provides some information about its projection. For example, it can mention Horizontal_Datum_Name: North American Datum of 1983, Ellipsoid_Name: GRS1980, Geographic_Coordinate_Units: Decimal degrees.
How do you determine the SRID? Doing the following query does not seem to work all the time (like this query itself returns no result)
SELECT srid, srtext,proj4text
FROM spatial_ref_sys
WHERE proj4text ILIKE '%nad83%'
AND proj4text ILIKE '%grs80%' AND proj4text ILIKE '%longlat%';