To register for the student membership with the SIAM organization, you may use this link: https://www.siam.org/membership/join-siam/individual-members
Click on Student (found in between Professional and Special Types), then click on the Join button found under the Free Undergraduate Student title.
It will first ask you to create a SIAM account. Once you have created a SIAM account, you'll be taken to a page with a Join Now button. From there, fill out the requested information about yourself. When you reach the Education portion of the registration process, please see the attached screenshot and make sure to fill out Institution, Chapter Name, and Start Date of membership exactly as given.