If I have a points file where the points share common attributes, what's the best way to draw a convex hull around those common points using QGIS?
First, you have to select the points that share a common attribute, either manually or with the "Select by expression" icon in the attribute table window (in that case, use the expression
"yourfield" = X, then click on "Select"):
Vector > Geoprocessing tools > Convex hull(s) and check the "Use only selected features" option:
This will create the convex hull you want. You have to repeat this process for each different value of the field.