LD_LIBRARY_PATH is optional if you include an entry in /etc/ld.so.conf for the library path: /usr/local/qt/lib, then run ldconfig to update /etc/ld.so.cache.
# note: configure has some options you can try, to see them
# see ./configure --help
# NOTE: when you run make as suggested on the next line, you may
# encounter a make error that halts the build IF you run make
# from outside X. The program $QTDIR/bin/uic (the User Interface Compiler)
# may Segmentation Fault when run from a Linux console. You can run
# "startx" and use the twm (tiny window manager) and xterm (or whatever you
# might have setup for X) to run the rest of the Qt build. If for some
# reason twm is not even available, then you can run "XFree86 &", use
# "CTRL-ALT-F1" to get to a console, start an xterm as
# "xterm -display localhost:0.0 &", then switch back to X with "ALT-F7".
# Only for old versions of Qt before 2.1.0 or so ...
# compile the opengl extension
# Note that in qt 2.2.0 on, the OpenGL support has been moved out of extensions
# and is now a standard part of the library that is installed if configure
# finds OpenGL installed on your system. If you were to not want OpenGL
# support in Qt, you'd have to pass the -no-opengl option to configure.
# Check the Makefile and ensure there are not Mesa references.
# Try compiling and running the examples.