How can I apply to become a master hunter, and what is involved?

See the WDFW Master Hunter Permit Program website. This website describes the application process, qualifications, and requirements in great detail.
The open registration period normally begins January 1 of each year, but length varies, so submitting your application early is recommended. However, applications will not be accepted before the open registration period.
There is a $50 fee required to register. Applicants are provided hard copy and/or electronic study materials to prepare them for taking a comprehensive 100-question examination.
Applicants have only nine months to finish all requirements, including but not limited to passing the test (only one retake allowed), and completing 20 hours of approved volunteer time.
There are very stringent zero-tolerance standards regarding convictions of fish and game regulations both prior to application and/or following certification.