You need an Amateur Licence to work satellites, but if you have not Licence at least you can receive they. It seems to be a very complicated thing to work one satellite or only for very good operators with sofisticated antennas and big transceivers... Really is like this but there are a lot of different satellites on the sky and you can contact a few just only with a Walkie Talkie!
Most easily I have worked are UO 14 (is a transponder, as a Repeater), PCsat (Telemetry and APRS Digipeater also Packet) and ISS, International Space Station which have on board a Small Packet PMS -Personal Mail System-, also works as APRS Digipeater and with a little o lucky you can contact with people on board, yes, most part of astronauts are Radio Amateurs with Official Licence.
For example I have contacted these stations with a simple vertical antenna and two equipments (one for TX and the other for RX, but if you have a Biband transceiver no need more) and 5 ó 10 w. is enought. ISS sometimes arrives here signal 9+20 and +30 Db.
You have other possibilities, you can decodify easily meteorologic Sat as NOAA on 137 Mhz
If you visit my Multimedia section you can listen a QSO with Space... There are a lot of satellites sent by Amateurs on the sky... Wath are you waiting for?
More info here.