Jupiter is among the easier objects to find and observe in the winter night sky. Just about any telescope and many binoculars can also see 2-4 of Jupiter's moons, just the way Galileo saw them in 1610. These moons, also called the Galilean moons, are Io, Europa, Ganymede and Callisto. The tool below, courtesy of Sky & Telescope magazine, will help you identify the moons you see.
If you are looking through binoculars or most refracting telescopes (eyepiece is on the end), the Direct view is correct. For newtonian telescopes (eyepiece is on the side), click on Inverted view to match the tool to what you are seeing.
Go back an hour later or so later, and the moons will be in a different position.
Galilean Moon Positions
Red Spot Position
For those with higher quality telescopes who can make out the red spot on Jupiter, this tool will help predict when the spot will be visible from Earth.