This is how i patch my jeans
First I turn the jeans inside out and cut out a bigger area than just the hole, usual the hole is in the knee area and I make the patch bigger so I am not sewing in the thinnest areas of the jeans, plus it makes sure the seam is not directly under my knee when I bend down to do something.
I cut a 45 degree anble in each corner of the hole, and then mark with a pin from the edge of the 45 degree cut all the way around to give me a guide where to sew

I cut a patch out of an other pair of donner jeans that is a little bigger than the hole I cut in the jeans.
I then pin the patch in place trying to keep it exactly flat and folded up towards me
then I sew around the seams making sure not to stitch other parts of the jeans together that do not need to be sewn to the patch.
once I have gone around the patch I come back and sew the corners, this makes a slight pucker on the patch and the jeans when it is done but it is not bad or really notifiable.
then I sew once more around the seam and trim the excess back with pinking shears
I iron the seams flat, turn the jeans right side out and iron the front of the seams.

more pictures

more photographs

done with the patch

I like this idea...Thanks for the detailed explaination and pictures. I haven't patched in awhile but always sewed by hand or had to rip open a seam.

Credit goes to mom, I watched her do this a million times during my growing up.

I bet she did not know I was paying attention

This is too cute not to share here, My son has gotten a little too old for these but might do some myself. http://insidenanabreadshead.com/2012/04/25/patching-knees-the-nanabread-way/