..it'll be the object engulfed in flames as it re-enters the atmosphere.

I realize not related to the space station, but still looking up in the sky at night, the most obvious thing is the moon ... and we just had a lunar eclipse, although it was not visible to folks in America. For anyone interested, I shot a few nifty pictures of the November 8th, 2003 lunar eclipse [komar.org] and I even have some cool Aurora Boealis pictures [komar.org] from 10 days earlier when it got as far down South as Colorado.

Another cool thing is Iridium Flares which are bright flashes of reflected sunlight from the Iridium satellite solar panels for 5-20 seconds - here is an excellent writeup about those including how to predict 'em! [satobs.org]

...is when you're trying to take a long exposure of the night sky. Sure enough, there's that tell-tale streak.

City dwellers don't see the ISS often, but go out to a good dark spot suitable for really examining heavenly objects, and you will realize just how many sattelites/orbiting objects are really up there, and how obvious they are.

I must admit, it was novel the first couple of times. At this point however, I'm beginning to advocate bases on the moon.

The space station is visible many times throughout the year. This website gives very accurate times for spotting it, and many, many other satellites.
http://www.heavens-above.com/

Current ISS position, updated every minute. [nasa.gov]

Yesterday in the office: I had my iBook beside me, running Celestia [shatters.net]. Try this: Current time, realtime, Select ISS, Go to ISS, Sync Orbit. Maneuver a bit around the station till you're where the Destiny module window is, then adjust the viewpoint so you get a nice horizon view. (Or just Track Sol.) Then just leave it running. Voila: anytime you feel like seeing what the ISS crew can see from Destiny, just look at Celestia. :)

(Interestingly enough, comparing the Celestia ISS view with the Station Location website, I found that Celestia's synchronization is a teeny bit off, but not by much. Nice work!)

If you watch the ISS pass overhead, or any other satellite, imagine that you have no idea what it is. Look for signs of unusual movements... see how it wiggles around in its path? You can really tell if you're in a moving vehicle -- it chases after you, and then suddenly it's gone!

GOTCHA!

When we went to White Sands, New Mexico [nps.gov], they had a guide show off the excellent view of the stars. He explained some basic astronomy, talked about relative distances and such, and then someone said, "what's that?"

It was a satellite, of course, and he played the trick above on the folks who hadn't watched one go across the sky before. He really had some of them going, too... I heard a few "hmmm!"s from the group as he described the light's perceived non-linear motion.

It gave him a great chance to explain why satellites get reported as UFOs, complete with unusual movements and sudden disappearances. The satellite is moving in a nearly perfect curve across the sky, but your head isn't a very steady viewing platform. And when a light in the sky (distance = way far) gets close to a tree or something (distance = well known), your brain perceives the motion as changing.

Hopefully, he gave the eastbound tourists something to think about on their way to Roswell [iufomrc.org].

Most importantly folks, this is a fantastic opportunity to go outside and yell "That's no moon! It's a space station!" at people who pass you on the street.

This ESA [heavens-above.com] page will give a personal timetable for ISS spotting.

Go here [sourceforge.net] to see when the ISS will cross in front of the moon or sun (use proper filtering on the sun!). Some results [sourceforge.net] showing considerable detail.

It's a space station!