11 minute video on drawing a pyramid pattern.
The above video describes the process of drawing a pyramid pattern. It does not show assembly. The demonstration includes a discussion on where tabs could go and why. All tabs are drawn freehand, but could just as easily be drawn with a straightedge.
The beauty of the arcing pattern is the circle that defines all of the equilateral triangles, making the process quick and easy.
At no point was a ruler used (instead, I used an unmarked straightedge), no numerical measurements were made at all.
The tools used are:

If you visualize a pyramid opening like a flower, you will notice that the square base is surrounded by triangles. Those triangles can be rearranged such that they are grouped together into an arcing pattern. This layout is simple to draw, and requires that only one edge is left to join at the peak, which makes it easy to assemble. If the pattern is drawn so that the triangles are built off of the square, then all of the glue seams run up to the peak, which is difficult to do.
Tab layout is a choice between ease of assembly and appearance. It is easier to assemble the pyramid if the square base is folded onto three remaining tabs than if the tabs have to tuck under the triangles. However, it is better looking if the reverse is done, and the tabs are bent up from the square base. In this second approach, the glue joint at the base looks more seamless.