Try the fun I had 10 years ago:
http://science.nasa.gov/newhome/headlines/ast22dec98_1.htm
It's very easy to do; I just sat perched a TV antenna (only thing I could get very quickly) on a camera tripod, and pointed it in the direction of Lake Kickapoo, Texas (very close to Wichita, Tx) with some slight elevation. Lots of very loud returns (had to dive for the audio control at times) during the shower, lots of short ones- a great visual as well as radio event.
As for Spacecraft, it was no sweat to pick up returns from the then small ISS. Just use your prediction program to predict when the station will pass through the beam (a huge, fan shape directed straight up), point your antenna at that point in the sky, and you will hear it if it is above the horizon at that moment at your location, and you are not too far away. The station is *much* larger now, so has a much greater RCS/larger return signal, so the horizon might be the only limiting factor now. I found the strongest signals occurred when the spacecraft was located in the NavSpaSur radar beam, and between my location and the transmitting ground site or nearer overhead and in the beam.
I used no preamp, and only the twin lead from the antenna directly to an Icom R7000 receiver.
The Shuttle was also quite audible. I did not try other spacecraft; remember these two are leo's.
I could not convince the author of the NASA article that the short fainter pings were not other satellites, even with simple math examples.
The receiving sites the government runs catch about 20,000 pings a day according to personnel.
73,
Steve W5ZA (located in Shreveport, La. -Northwest Louisiana, about 300 miles east of the radar site)