Drawing surfaces in Sketchup
Drawing surfaces in Sketchup is easy and intuitive to a degree you won't find in other design apps--even costly ones.
You can begin creating surfaces (and then objects from those surfaces) by clicking the pencil tool on the main toolbar. After selecting the pencil, drag it over the main window, and watch carefully how the line segment you're forming takes on different colors. These colors represent parallel alignment with the x, y, or z (width, length and height) reference axis. Notice also how the segment snaps to the axis.
Drawing edges in Sketchup
To create an object from edges, first form a plane, AKA "surface," made of a series of line segments, whose last segment connects with the first. Sketchup confirms that you've made a valid plane by shading the plane. After you've made a plane, select the "Push/Pull" tool, then click the plane and drag a line perpendicular to it, to pull (AKA extrude), the plane into a three dimensional shape.
Before and after: Sketchup confirming successful plane creation
Tip: Sketchup makes it easy to create planes whose sides are of equal length (parallelograms) by using invisible grids that your pointer snaps to. Draw two sides of a rectangle, and then begin drawing the third side. As you trace the side, Sketchup will highlight where the endpoint of the segment should go.