How to install and run qt-designer for python

with sudo apt-get install python-qt4 qt4-designer should work.

You can find it if you search it with apt-cache search qt | grep designer:

libqt4-designer - Qt 4 designer module
libqt4-designer-dbg - Qt 4 designer library debugging symbols
qt4-designer - graphical designer for Qt 4 applications
kdesignerplugin - Integration of KF5 widgets in Qt Designer/Creator
kdesignerplugin-data - Integration of KF5 widgets in Qt Designer/Creator
kgendesignerplugin - Integration of KF5 widgets in Qt Designer/Creator
libopenrpt-dev - graphical SQL report writer, designer and rendering engine (development)
libopenrpt1v5 - graphical SQL report writer, designer and rendering library
libqscintilla2-designer - Qt4 Designer plugin for QScintilla 2
libqscintilla2-designer-dbg - Qt4 Designer plugin for QScintilla 2 (debug)
libqt5designer5 - Qt 5 designer module
libqt5designercomponents5 - Qt 5 Designer components module
libqt5scintilla2-designer - Qt5 Designer plugin for QScintilla 2
libqt5scintilla2-designer-dbg - Qt5 Designer plugin for QScintilla 2 (debug)
libqxt-designer0 - LibQxt extensions to Qt Designer
openrpt - graphical SQL report writer, designer and rendering engine

And search more info about the package with apt-cache show qt4-designer.

type on your Terminal

designer-qt4

or if /usr/bin isn't included in your PATH:

/usr/bin/designer-qt4

Considering the packages names did dramatically change, the procedure with Ubuntu 20.04 is now:

sudo apt-get install qttools5-dev-tools
sudo apt-get install qttools5-dev

Then Qt Desginer is installed as designer, and is also in the start menu.

Credits