Permits can be submitted online through MyBuildingPermit.com.
Sammamish PDF Submission Requirements
Google has created a sketching tool that may be useful to you in the application process.
Public Works Department
Although the city handles most types of permits, the assistance of other agencies will be required to issue permits and inspect specific aspects of a project:
Water and Sewer
Septic and Wells
Special Use Permits
Permits & Regulations