Short answers, pulled from the story.
Nixon's visit to China lasted from the 21st to the 28th of February, 1972, a total of seven days. He traveled to Beijing, Hangzhou, and Shanghai, departing China on the morning of the 28th on a flight to Anchorage, Alaska.
Nixon visited China primarily to gain leverage over relations with the Soviet Union, following the Sino-Soviet split that began in 1956. The visit also served as pressure on both the Soviet Union and China to reduce their support for North Vietnam, making resolution of the Vietnam War a key motivation.
Mao greeted Nixon by saying, through his translator, "I believe our old friend Chiang Kai-shek would not approve of this." He also joked "I voted for you during your last election," to which Nixon replied that Mao had voted for the lesser of two evils. Mao responded that he liked rightists and was comparatively happy when people on the right came into power.
The Shanghai Communique was jointly issued by the United States and the People's Republic of China on the 27th of February, 1972. Both nations pledged to work toward full normalization of diplomatic relations and acknowledged longstanding differences over Taiwan, temporarily setting aside the question of Taiwan's political status to open trade and other contacts.
In July 1971, Kissinger secretly traveled to Beijing during what was publicly presented as a trip to Pakistan, where he met with Chinese Premier Zhou Enlai and laid the groundwork for Nixon's visit. Pakistan arranged and facilitated the meeting through its strong diplomatic channels with China. Nixon had also conducted years of carefully calibrated moves through intermediaries Romania and Pakistan before Kissinger's secret mission.
Within a year, U.S. allies including Japan, Australia, and West Germany broke relations with Taiwan to establish ties with China. Full U.S. diplomatic recognition of the People's Republic of China came in 1979 under President Carter. The visit also inspired John Adams' 1987 opera Nixon in China, generated the lasting political metaphor of a "Nixon to China" moment, and played a role in opening China to U.S. trade.