Here are links to ASA Citation Style sources. Thanks to Diana for the first one!
Preparation Checklist for ASA Manuscripts - 2 page quick reference guide (This guide does not include how to cite articles from an electronic database.)
Purdue OWL - ASA (Purdue also does not include how to cite articles from databases!)
Cal State LA's guide - detailed and with in-text and references list examples, including how to cite an article from an electronic database
There does seem to be some discrepency about how to cite an article from an electronic database. The university library guides that are dated and identify which manual they referred to all seem to concur with the format on Cal State's guide. The basic format is:
Author Last, First. Year of Pub. "Title." Journal Name volume # (issue #):
inclusive page numbers if available. (Retrieved from Database Name
on Month Day, Year of Access.)
However, other guides had slight differences in the punctuation and language used to identify the database. We do not have a copy of the American Sociological Association Style Guide, so I can't check it against the manual.