The moons of Jupiter can be observed using a telescope, even a small one, as they are relatively bright and large compared to other celestial objects. The four largest moons, known as the Galilean moons (Io, Europa, Ganymede, and Callisto), were discovered by Galileo Galilei in 1610 and can be seen as small points of light near Jupiter. Binoculars can also provide a view of these moons, although details will be limited. For the best experience, observing during a clear night with minimal light pollution is recommended.
With a telescope
Please see related question for a complete listing of Jupiter's 40+ moons.
You would not be able to see the moons from the surface; Jupiter's atmosphere is too thick.
The moon we see doesn't, but all of Jupiter's moons do. (About 50)
You can see Jupiter's moons any night whenever you can see Jupiter, with the possible exception of times when the Moon is close to it. Just now (2014) Jupiter is mostly visible in midwinter.
Jupiter has 63 confirmed moons. See link for further information about them.
He saw 4 moons
Yes, it is possible to see Jupiter's four largest moons, known as the Galilean moons, with just a pair of binoculars or even with the naked eye. These moons are Io, Europa, Ganymede, and Callisto.
Jupiter's many moons
Jupiter's moons do not have moons. No moon in the Solar System has a moon orbiting it.
Yes
because there are a lot of moons that surround Jupiter and they rotate around Jupiter at different paces not all can be seen at the same time