When creating a polygon, how do I do it so that the lines are straight (90, 0 degrees, etc.) and when I create corners they can be right angles? For instance, how do I create a perfect square or rectangle?
No plugin needed
In addition to the Shape Digitizing Toolbar it's also possible to add right angles through the Advanced Digitizing Tools.
Activate the Advanced Digitizing Tools and lock the angles to 90° . Have a look at the documentation of the advanced digitizing tools for what else is possible.
With QGIS 3.14 the last missing bit was added and it is now possible to snap to the currently digitized feature which makes it possible to finalize an object with a right angle. Note the keyboard shortcuts to lock the angle which are shown in the demo video below.
I tried the suggested solutions but found the CADTools plug-in a bit too complicated to get a quick hang of it. Besides, this is a rather simple task.
Instead I found the plug-in Rectangles Ovals Digitizing￼ by Pavol Kapusta. The name is rather self explanatory and it works excellently. You can draw shapes from centre or by extent.
the CadTools plugin should do what you want. there is also an tutorial: http://www.catais.org/qgis/cadtools/ (especially look under "orthogonal digitzing")
Another solution is you use the plugin azimuth and distance. http://geotecnologias.wordpress.com/2012/02/03/criando-poligonal-por-azimute-e-distancia-qgis/
In order to create polygons or lines with specified lenghts en angles you need to enable the advanced digitizing panel. (View--panels-advanced digitizing)
Just add vector layer (lines or polygons) start editing and add feature. In the advanced editing window you can specify the angles and/or distances. To finish the sketch, click right mouse.
I tried the CADtools but I found it a bit complicated. Besides, this is a rather simple task.Instead I found the plug-in Quantum Aided Design(cad like commands in QGIS). The name is rather self explanatory and it works excellently. You can draw/edit/copy/ trim or offset etc..