How to design a neck-down shawl

Many popular triangular shawl designs are started at the neck and worked down to the hem, in two triangle-shaped sections with a center stitch down the middle.

The basic chart for one triangle (i.e., one half) of this shawl looks like this:

The grey cells in the chart indicate "no stitch". I've shown the number of stitches in each section in green -- you can see how the rows increase in size every other row using yarn-overs at the beginning and end of the section.  You could use this section to start a shawl like Birch that is knitted from the tip up.
To get a neck-down shawl with a straight edge along the top, you need to add two of these triangles together. In the case of the Flower Basket shawl, the designer added a row of garter stitches, two stitches wide, as the border at the top of the shawl.  You could make this border wider if desired, and/or make the center stitch wider, if you cast on a wider starting row.
This is what you get from the above chart, after knitting a few rows:

By combining four triangles instead of two, you can design a square shawl knitted from the center out.

If you want to insert a design element, you need to find something that fits in this triangle.  For instance, try inserting a simple Shetland quatrefoil eyelet.

In this example, the even rows are not shown, because they are all plain (i.e., no pattern elements).

The pattern repeat is shown below with a bold border.

You can insert other designs; the easiest ones to use will be the ones that are "square", i.e. as many stitches wide as it is tall.