One light-year is 9,460,730,472,580.8 kilometres — about 9.46 × 10¹² km. The value is exact rather than measured, because both the speed of light and the length of the year used in the definition are fixed by agreement.
About the units
A light-year is the distance light travels in vacuum in one Julian year. Two exact constants go into that: the speed of light, fixed at 299,792,458 metres per second when the metre was redefined in 1983, and the Julian year, defined by the International Astronomical Union as exactly 365.25 days of 86,400 seconds each. Multiply them and the result is exact to the last digit. It is worth stressing that a light-year measures distance and not time, despite the name — a mistake common enough that science fiction gets it wrong regularly. Astronomers themselves mostly prefer the parsec for professional work and reserve the light-year for public communication, where its meaning is more immediately graspable.
The exact factor
The derivation is one multiplication: 299,792,458 m/s × 365.25 × 86,400 s = 9,460,730,472,580,800 metres, or 9,460,730,472,580.8 km. For a sense of scale, light takes about 1.3 seconds to reach the Moon, 8.3 minutes to reach the Earth from the Sun, and about 4.2 hours to reach Neptune's orbit. The nearest star system, Alpha Centauri, is 4.25 light-years away, which is roughly 4 × 10¹³ kilometres — a distance no spacecraft built so far could cross in less than tens of thousands of years.
Where you meet this conversion
Popular astronomy uses light-years almost exclusively, because the alternative is a number with fourteen digits that conveys nothing. Distances to stars, nebulae and galaxies are quoted this way in every observatory press release. The unit also carries an idea that kilometres cannot: because light takes time to arrive, looking at something a thousand light-years away is looking a thousand years into the past, which is why deep-space images are described as views of the early universe.