Kili Technology allows to quickly position polygons. To do so, select the object you want to annotate, and click to place a vertex. You can easily cancel the annotation or undo the last vertex positioning. To finish the task, just close the polygon by clicking on the first point positioned. The form will be consisting in the inside of the polygon you built. If you don't want to deal with closed form, see polylines.
It is also always possible to change the class of an annotation with a left click, selecting "Change class", and then select the new class of the object. If the task is multi-classification, this operation will allow you to select all the categories for this annotation : you can delete the previous class but also just add one or more others.
Polygon can be nested (see nested classification)) with all classification tasks, to build refined object classification.