How to import a non-spatial Table into QGIS?

Sure thing. Just load it via the Add Vector Layer button. It's not really a vector layer I know but that's just how it's coded at the moment.

Since QGIS 2.6 (at least since mmqgis tools were imported in the main menu) this is done by the menu

Layer > Add layer > Add Delimited Text Layer

Browse to your file in the File name field

Under Geometry Definition, choose "No geometry (attribute only table)"

Relevant section in docs: Importing a delimited text file

You can import a csv file and make a join by attributes with the mmqgis plugin.

Extension > Mmqgis > Attributes join from CSV file