"Visit the bank office in person and apply for a bank account. The bank will want to know how you are connected to Estonia and how you plan to use the account. You will need to bring your e-residency card along."

In terms of opening a bank account, SEB now offers a way to do that through a video meeting: http://www.seb.ee/eng/remote-advisory, although right now if you're not yet a client, you can not use it. They promise to open it up for new clients as well, but no ETA I think.