Have you ever seen an asteroid? It's more fun — and much easier — than you might imagine. If you're new to the game, then Vesta, the brightest of the lot, is definitely the one to start with.
This is a great time to view Vesta, because the asteroid is directly opposite the Sun, and almost at its brightest and closest to Earth, on October 29, 2008. It remains quite bright through mid-November, then fades gradually toward the end of the year. But even on December 31st, Vesta will still shine brighter than any other asteroid ever gets throughout 2008.
Vesta is near the head of Cetus, which rises an hour or two after sunset in late October. You will get your best views when the asteroid is high in the sky, which won't happen for another couple of hours after that. But by late November, Vesta will already be quite high by the time the sky is fully dark.
In 2007, Vesta got just about as bright as it ever can, reaching magnitude 5.4. At that point, I could spot it easily from a dark location with just my unaided eyes. It will be much tougher to see naked-eye this year at its peak magnitude of 6.4. But it's a snap to find with binoculars. Just click here to download a printable chart in PDF format. Then locate the head of Cetus and start comparing what you see through the binoculars with what's printed on the chart. When you find a medium-faint "star" that isn't plotted on the chart but is on Vesta's track — you've found the asteroid! The chart shows stars to magnitude 7.5, Vesta's brightness in the last week of December.
What's so fun about viewing something that looks just like any normal 6th-magnitude star? To find that out, make a little sketch of how Vesta fits into the surrounding star field. Then come back a night or two later, look again, and you'll see that the asteroid has moved. Vesta is moving about ¼° per day, so its motion is quite obvious over a course of a few nights.
Through a telescope at medium to high magnification, Vesta's motion is obvious over much shorter time spans. The asteroid covers 0.6 arcminutes per hour, which is a substantial distance at 100×. Try it; I bet you'll like it!