SPU databases will link to SPU full-text quite automatically. Those on the open Web will not. So use the latter (Google Scholar only excepted) in conjunction with Finding the Full Text.
Seattle Public Library and King County Library System databases are accessible to anyone with SPL and KCLS accounts. University of Washington databases you must be in a UW library to use. In addition to the UW databases listed below, consider also those listed on p. 2 of the course handout.