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.
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:
All Electrical Permits and Boilers in Excess of 200K Btu/h
Water and Sewer
Septic and Wells
Permits & Regulations