Sketch out a design focusing on shapes that extend to the edge of your paper. I went to Google.com/images and searched for "Queen Anne's Lace" for my inspiration. My sketch is very loose since I intend to cut most of the details freehand.
Once you have sketched your design, fold your thank-you letter down to its final size and press firmly along all creases. Unfold. (Note: creasing your paper BEFORE you cut it is many times easier than creasing it after it's cut.)
Use a scissors or craft knife to cut out your design. It's sometimes easier to begin by cutting the perimeter silhouette before focusing on other details.
Try to keep your designs loose and unfussy. This note was done mostly freehand and took just over an hour to cut out.