Use heavy-duty wash-away (water-soluble) stabilizer.
Load hoop into your embroidery machine, set threads, and load the design.
Stitch the first placement line on your stabilizer.
Then, place your base fabric on top of the line, and stitch tacking stitch.
Trim and then stitch the patch interior, followed by the final border stitch.
Remove the hoop from the machine and tear out the patch.
Fuse iron-on backing or finish the backing however you prefer.