Where in Qt Creator do I pass arguments to a compiler?

Depending on your build system it's either in your qmake project file(.pro, standard for new projects) or in one of the CMake files (CMakeLists.txt, used by KDE and several other projects).

Using .pro:

QMAKE_CXXFLAGS += -O2

Using CMake:

set( CMAKE_CXX_FLAGS "-g -Wall")

To add compiler flags, open your .pro file and add a line like this:

QMAKE_CXXFLAGS += -std=c++0x

For standard flags like debug vs. release etc. you should try to use the predefined qmake options (see QMake documentation) for the sake of platform and compiler-independency, as QMake will map them to the compiler-specific flags.