I am trying to draw two squares on a 45-degree angle and then merge them using PostGIS to edit. QGIS can draw squares but only on a perpendicular plane (eg, 0, 90, 180), and I need to be able to draw at different angles (eg, 45-degrees).
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I googled "qgis diamond" and found that there is a plugin that will supposedly do this. Go here: http://pyqgis.org/repo/contributed and scroll down to "Rectangles, Ovals, Diamonds : 0.1.7". Haven't tried it though.
What you want to do is called Digitizing or Editing. Have you looked at the digitizing toolbar? Also have a look at the Digitizing an existing layer section from the Qgis user manual.
You can create new features in various types of vector layers, including a PostGIS layer.
You should add your PostGIS data to your map, and then toggle editing. After that you can start digitizing and adding new features.