For invisible machine applique, the usual process involves tracing your design onto a lightweight piece of sew-in interfacing, (remembering to reverse the design where necessary), stitching it to the fabric, then cutting a small opening in the interfacing to turn the applique right-side out. You smooth out the design using a turning tool/point turner, then give the applique a good press. A spritz of ironing spray also helps with crisp applique shapes. The applique is then glue basted to the background, lightly touched with an iron and allowed to set for a few minutes. Then, the design is stitched down using a narrow zig zag and invisible thread.
Applique stitching particulars:
For glue basting, investing in a bottle with a micro tip is well worth the money. I bought a bottle of Appli-Glue with the micro-precision tip that allowed me to twist on a different cap for travel. The glue part of the product works well, but I’ll probably refill it with good old Elmer’s washable school glue once it runs out.
Use a fine point mechanical pencil for tracing designs (.5 lead size)
Test a variety of sheer and light-weight sew-in interfacing to see which one you prefer. I tried Pellon 905, 910 and the Lori Holt versions. Personally, I prefer Pellon 830, which is marketed as pattern tracing cloth. It’s a poly/vicose blend that feels similar to Lori Holt’s product, but is a little bit lighter weight.