You need a Windows PC. At present, Symbian development is best supported on Windows XP and Windows Vista.
You need an Symbian SDK that matches the phone you want to develop for. The SDK includes documentation, headers and libraries for the Symbian platform as well as the tool chain for building C++ based Symbian applications. It also contains the Symbian device emulator that lets you test applications on the PC before deploying them to a phone.
Note: The technology used in phones progresses quickly which means there are frequent releases of the Symbian platform to support the new technologies. It is perfectly okay to install several SDKs to develop for different types of Symbian phones.
Install Carbide.c++ Integrated Development Environment
You need Carbide.c++ 2.0.2 to do Qt for Symbian development. Qt support has been integrated with Carbide.c++ so you can read .pro files and develop UIs with the built-in Qt Designer functionality. The Carbide.c++ distribution also includes the compiler for building C++ applications that will run on the Symbian emulator on your PC rather than deploying them to the phone.
And of course you need Qt for Symbian. There is a special distribution of Qt 4.5 that has been ported to Symbian. The package includes a set of pre-built binaries so you don't need to build Qt from source (although you still can if you like).
Once Qt is installed, Carbide.c++ needs to be configured so it can find your Qt installation.