To get my patch, I had to use a seam ripper to rip off the patches from my shoes and give it a good wipe clean. I was actually quite surprised to see double-sided tape underneath but couldn't discount the quality of my shoes too much since the patch was sewn on as well, but I digress.
Step 1: Lay the blazer flat onto an even surface and align the crest/patch accordingly. If your blazer has stripes, use this as a guide.
Step 2: Sew the outer most points symmetrically. So for this case, I sewed the top of the cross first, then then the widest points of the crown, then the two bottom corners. If you sew around, you run the risk of mis-aligning the crown in the process.
This DIY technically cost me nothing as the blazer was gifted and the patch was obtained from my shoes. I plan on making more of these are I still have the patch from the other shoe and vintage patches from when I used to collect them, one being quite similar to the patch on the middle blazer image above.