Since Yuri Gagarin's spaceflight in 1961, more than 400 humans have gone into space. The method of getting there has changed little in that time, though the rockets have gotten more powerful and complicated. The basic requirement is a rocket with enough power to overcome the pull of Earth's gravity, and enough speed to stay in orbit and not fall back to Earth.
There are currently only two vehicles capable of taking humans into space: the Russian Soyuz TMA spacecraft and the U.S. Space Shuttle. The Chinese are developing a spaceship, but it's still in the testing phase. With the space shuttle program on hold until the Columbia Accident Investigation Board completes its report, only the Soyuz spacecraft remains.
The Soyuz was originally designed to take crews to and from Russian space stations. A Soyuz flew to the world's first space station, the Russian Salyut 1, in 1971. A modified version of the original Soyuz now performs that same service for the International Space Station. It also serves as the space station's lifeboat should the crew ever have to abandon the station.
The Soyuz is launched from the Baikonur Cosmodrome in Kazakhstan aboard a Soyuz rocket. A Soyuz taxi crew normally delivers a new Soyuz capsule to the space station every six months. The taxi crew then returns to Earth in the older Soyuz capsule, which was already at the station.