On the morning of April 5th, 2063, it was passing through the outskirts of the Sol system, when it detected Dr. Zefram Cochrane's warp signature during a test flight of the Phoenix from the vicinity of Earth, a planet which the Vulcan High Command had been monitoring for decades. As per Vulcan first contact protocols, they decided to land on Earth, to meet the person who flew the first warp ship of their world. They landed in Bozeman, Montana. (Star Trek: First Contact; ENT: "Desert Crossing", "Carbon Creek")
The commanding officer of its three-person crew exited the vehicle first, and offered the Vulcan salute, "Live long, and prosper." Dr. Cochrane tried and failed to perform the same hand gesture, so he shook the Vulcan's hand and thanked him. The Vulcans and Dr. Cochrane then went into the local establishment for beverages, and a presentation of the local music, with an invitation to dance along to "Ooby Dooby" by Roy Orbison. (Star Trek: First Contact)
The Star Trek Customizable Card Game identified its captain as Solkar, who later went on to become the first Vulcan ambassador to Earth. Mike Sussman used this information when writing "The Catwalk", though the final line as it appeared in the episode is ambiguous.
According to the RPG sourcebook The Way of Kolinahr, the Vulcan ship that made first contact with Earth was called the Vesaya and its captain was named Sevak.
The Hidden Universe Travel Guide: Vulcan suggested that the T'Plana-Hath would go on display at the T'Plana-Hath Historical Museum, a Smithsonian Air and Space Museum-like Vulcan museum in ShiKahr. (p. 31)