These actually look harder than they are...you can strip piece the diamonds. Sew strips of your chosen colors together, then cut into strips of diamonds. Match seams and sew the strips together. If you have trouble getting the seams to line up, hold them in place with a drop or two of basting glue at each intersection (hit it with your iron to dry/set the glue) before sewing.
You'll need to make a drawing showing where you want each color, and organize your strips so the colors land where you planned...that's the major tricky bit, but if you stay organized, it goes together very easily.
Here are a couple of many tutorials I found with a quick look on the internet:
http://www.angelfire.com/va3/jclane/LoneStar/LoneStar.html
http://hopefulhomemaker.com/wp/2013/04/01/lone-star-block-tutorial/
Also, be careful not to stretch the bias strips of diamonds. As Margo always says, starching the fabrics heavily before sewing and cutting will help stabilize the shapes and edges.