The best place to start is to call the Salem-Keizer Schools district office and confirm the current policy and procedures for attending a school in a different "attendance area" within the Salem-Keizer district. A different "district" would be one like the Gervais School District, the Silver Falls School District, or the North Santiam School District. "Attendance areas" are for individual schools within the same district (e.g., McNary HS attendance area, Parrish MS attendance area, etc.).
Salem-Keizer calls attending a Salem-Keizer school outside of the student's assigned attendance area an "in-district transfer," and has some information (with a publication date of June 2003) on the district's web site: http://www.salkeiz.k12.or.us/search/apachesolr_search/indist
Because at this point you are only contemplating an in-district transfer, and the in-district transfer would NOT be from your current attendance area, it's likely that the district will ask you to initiate your written request through the principal's office of the school where your new home would be located. Again, you should confirm this by calling the district office: 503-399-3000.
Like Melina (below), my past experience is that the S-K district is accommodating when it can be. For example, I have one former client who lives in east Salem in the attendance area for McKay High School, but the district allows the daughter to attend South Salem High. The drawback, of course, is that the family has to find their own transportation for the daughter, which is more costly than taking the local school bus. For your student, it would also be more time-consuming if he/she weren't able to drive.