You can get your Estonian Student Identification Card from the dean’s office of the faculty you are registered to, starting from the beginning of the semester. Check your admission letter or SIS to identify the faculty. Please take one photo in a standard size with you. The card is a generally accepted form of student identification in Estonia.
It is also possible to get an International Student Identification card (ISIC) that proves your student status all over the world and gives discount in more than 700 places in Estonia.
You can apply for the ISIC card online on https://www.minukool.ee/en/content-with-menu or at the SEB bank or Swedbank (to get ISIC card with debit card functions: http://www.seb.ee/eng/everyday-banking/debit-cards/isic-and-itic-cards or https://www.swedbank.ee/private/d2d/cards/debit/isic). ISIC card reaches to student in 10 days.
Note that the Student Identification Cards are not the same as Student Library or Student Sports Centre cards, and will not grant access to the library or athletic facilities.