As STS-119 works on loading a new truss and solar panel set on the International Space Station, it all seems like science fiction, removed from human contact. However, spotting the ISS and Shuttle is actually pretty easy, and you can do it with the naked eye!
I actually found that site a bit difficult to read (for example, one pass for me is listed as being at 08:47 p.m., which is a confusing way to phrase it). So I actually recommend you go to one of my all-time favorite sites on the web, Heavens Above. Enter your latitude and longitude (you can get those from any number of sources, including Google maps), and away you go. You can find out when all manner of satellites are visible from your location, and even get sky maps to help you spot them. It's a phenomenal website, and the first one I go to when I know I'll be out at night.
Not to diss the NASA site, of course. They do have a very nifty map showing the real-time location of ISS right now which is pretty slick. You can also use the N2YPO site that has real-time maps of where a ton of satellites are, too.