Step 3: Make it an iron-on.

Picture of Make it an iron-on.
This is the trick that makes it easy. I don't have patience for all that careful fiddly pinning-before-you-sew business, so double-sided fusible web rocks my little haphazard-seamstress world. I use double-sided 1/2" fusible web tape, which you can find at most fabric or craft stores.

Cut strips of fusible web tape such that you can line the edges of your patch. The tape has one side that's exposed and slightly sticky and one side that's covered with paper; press it sticky-side down onto the back side of your patch. Run a hot iron over the paper-covered tape for 5-10 seconds to bond it to the fabric, let it cool briefly, then peel off the paper.

You should now have a DIY iron-on patch.