The Justices communicate by exchanging written memoranda, or at least they did during Justice Stevens’ time. See Jeffrey Toobin, The Nine: Inside the Secret World of the Supreme Court (2007), p 48:
Outsiders tend to be surprised by how rarely Supreme Court justices speak to each other, one on one. Under Rehnquist, the nine spent a good deal of time together as a group. Argument days, most Mondays and Wednesdays when they were in session, were preceded by the traditional thirty-six handshakes, each justice with every other, and they had lunch together most of these days as well. There were also conference discussions every Friday during these weeks. After the conference, however, the justices tended to communicate with one another through memos, which were often drafted by their law clerks. (After e-mail became ubiquitous, the memos also circulated electronically, but always with paper copies as well; among the justices, only Thomas and Breyer, and eventually Stevens, were fully comfortable communicating by e-mail.)
Some further detail about the distribution of these memos appears later in an anecdote about Bush v. Gore (p 170):
Stevens drafted an order of just a few sentences remanding the case to the Florida Supreme Court for the setting of a statewide standard to continue the recount. He sent his messenger scurrying down the marble hallway to Kennedy and the rest of the justices. He heard nothing back, except from Ginsburg, who said she would join if it was a way of bringing the whole Court together. (The rush of events in Bush v. Gore strained the Court's technology, which was, in 2000, still rather primitive. As a security precaution, the e-mail system circulated only within the building. Plus, there was only a single, communal computer from which the justices and clerks could obtain access to the Internet. Because only Thomas and Breyer used computers regularly at the time, there was little pressure from the justices to update. For the most part, the justices communicated with one another by hand-delivered memos, which were typed by their secretaries.)