Fundamental Vector GIS procedures
Fundamental vector GIS procedures are mostly about drawing on maps. Vector elements are a bunch of relatively simple line, point or polygon elements that convey some information to the information. Sometimes you can derive these from raster data (for example in a contour shapefile), in other cases it's generated from attribute data from a map (number of habitants per some area) and in other cases you draw it yourself (tracing a road on a map).
You may ask the question:"Why not simply draw over a map in inkscape, isn't that also a vector drawing tool?". Those tools are not georeferenced, so next time you make an orthophoto in the same location and that has a slightly different GSD and/or area, your vector shapes that you took so long to create won't fit and you need to draw everything again.
Create a layer
Click the "New shapefile layer" function in QGIS. Specify a sensible CRS. Specify if you want to create points, lines or polygons in this layer (you cannot mix, unfortunately). As soon as you select the feature type, you should also provide "attributes", which provide additional data on each point, line or area. These attributes are useful later, because they can be used to change your display properties on the fly. For example color areas < 100m2 blue, between 100-200 yellow and above 200 red.
Save the shapefile.
Add features
You can now start adding features manually by drawing on the map. In QGIS, you need to click the pencil icon first to start editing. In the same bar, there are additional tools to change the feature nodes and move the entire feature.
Stylize the feature
Define the colors, label the features, apply rule-based styling, there are a host of possibilities here.
Extended tutorials
http://docs.qgis.org/2.8/en/docs/training_manual/create_vector_data/index.html