The QGIS Workshop is web-based tool for learning the basic tasks in QGIS. See also the series of video modules in QGIS linked from the Workshop pages or listed below.
1. User Interface, Open Layers, Selection Youtube
2. Selection Tools Youtube
3. Projections, Adding CSV, & Heatmap Youtube
4. Point in Polygon Youtube
5. Table Join, Spatial Join, and using CSVT Youtube
6. Distance Matrix and Summary Join Youtube
7. Buffer, Difference, Clip Youtube
8. Georeferencing Historical Maps Youtube
9. Cartography Tutorial for Print and Web Youtube
10. Editing Vector Layers (version 1.7) Youtube
11. Batch Reprojection with Processing Youtube
12. Using R within QGIS Youtube