If you don't have an account, register for one. If you have one, login.
Scroll through the calendar until you see the month of the performance you want to attend.
For the performance, select either "in picture," which will show you the theater with the available seats represented by colored dots, or "in table," which will allow you to choose tickets by price and section.
Select the dot(s) for the seats you wish to purchase or check the seats from the list, and click "Add to Basket."
Review the summary and confirm the order.
Once confirmed, you'll get a confirmation number.
Choose the payment method. If "cash" is an option, you must pick up the tickets within the time it says on the site, or they will be released. (Usually within 3 days.)
If you choose credit card, you will pay through the ASSIST site (which the Mariinsky also uses).
If your card has gone through, the confirmation page will show this in red type at the top of the page.
Print the "confirmation certificate" from the confirmation page, and bring it with you when you pick up tickets at the box office.
If you are not also bringing the credit card you used to make the purchase, jot down the last four digits of the credit card on the certificate.