I am still surprised that a lot of people don't know that man-made satellites can be easily visible to the naked eye. Not only that, but they're predictable. Of course!
The International Space Station, or ISS, is orbiting the Earth at the same time the Earth is spinning and orbiting the Sun. The combined motion can be quite complex, but totally predictable. And right now we're having a "good sighting season": the orbit of the ISS is keeping it near the terminator, the division between day and night on Earth. That means it's up high and lit by the Sun even when it is getting dark (or before sunrise) on Earth.
If you want to see it, go to Heavens-Above and register, entering your latitude and longitude. You can then see when the ISS (and lots of other objects) are visible from your location. In general, you might get a few passes during the next week. However, like I said, this is a good time to look; this is what I saw when I entered my location:
Whoa! I've never seen that many passes in one week! But don't be daunted; reading the table isn't hard. The left and right column show rise and set times for ISS and aren't all that useful; it just gives you an idea of when to be outside looking. However, when it's really low on the horizon it's very far away, quite faint, and moving slowly.
The middle column tells you when it's highest off the horizon (maximum altitude). For me, for example, tonight as I write this it will reach maximum height at 9:25:52 p.m., when it will be 46 degrees above the horizon, or about halfway from the ground to the zenith. That's not bad, and it'll be at a magnitude of -1.2, or pretty bright, outglowing all the stars in the sky (and even the handful of planets up right now at the same time).
The azimuth tells you what direction to face to see it: for me, it'll rise in the west-southwest, hit max at north-northwest, and set in the northeast. If I go out tonight to watch it (unlikely; it's pretty cloudy) I'd go out three or four minutes early so that I don't miss it, and my eyes have a couple of minutes to adjust to the darkness. Earlier is better, so you are more dark-adapted.
Although I am no fan of the ISS, it is very pretty go see, and an amazing thing if you've never seen it before. You can even get pictures! If you do, post 'em on BAUT, too.