A "conference call" was the term used by Madame Vastra for a psychically-induced conversation across time and space. According to Vastra, time travel had always been possible in dreams, allowing the unconscious mind to transcend time and space, while the body remained where it was.
On one occasion, Vastra and Jenny set up a conference call to discuss information pertaining to the Eleventh Doctor Vastra had obtained from interrogating Clarence DeMarco in prison in 1893 London. They requested the presence of Strax and companions Clara Oswald and River Song.
One had to be unconscious and dreaming in order to attend the conference call. Vastra and Jenny achieved this by inhaling smoke from candles instilled with a soporific which rendered them unconscious; Vastra sent a similar candle, along with a letter, to Clara at her home in 2013. Assuming she would not trust Vastra enough to use the candle, though, she also soaked the paper of the letter in same soporific; merely handling the paper would put Clara to sleep. Strax simply had a man knock him unconscious with a shovel. Its unclear how River entered the call being a data ghost.
The call Vastra assembled represented a round table in a room with rapidly swirling colours on the wall; Vastra mentioned that she had changed the "desktop theme", having grown tired of the "Taj Mahal". Vastra showed the ability to serve tea (drawn from one of her favourite memories), which River was able to turn into a glass of champagne; Vastra was also able to use a sand-like material to display images such as Clarence's conversation with her, and a series of space-time coordinates written in Circular Gallifreyan.
The call ended when the Whisper Men attacked Jenny's body within Vastra's house, killing her. Realising they were under attack, River commanded everyone to wake up, slapping Vastra and throwing her champagne in Strax' face. Upon waking, Vastra and Strax found themselves surrounded by Whisper Men and kidnapped. The Great Intelligence suddenly interrupted the call and left a message that the Doctor would have to go to Trenzalore to rescue his friends. At this point, Clara woke up naturally, hearing the Doctor calling out in her sleep.
Clara and River remained psychically linked for several hours after the conference call ended. River said this was because she left "the line open" between her and Clara. River was able to use this to guide Clara across Trenzalore and the Doctor was somehow be able to see her too despite River only being linked to Clara. The Doctor was able to use this to say a final goodbye to River, something he had been avoiding and River realised that Clara was still alive because River could only exist there because of her link with her. After telling the Doctor this, River ended the "call" and faded away for a final time. (TV: The Name of the Doctor)