This is another Grammaw-inspired lesson. She never really sat down and showed me how to patch the knees of my blue jeans, but I was quite the little tomboy growing up so I had ample opportunity to see how it was done from the patches she, and Mom, put on my own blue jeans. This method works great - repairing the hole and reinforcing the entire knee area. It feels good to wear, blends right in, and gets softer right along with the pants over time.
If a hole is in the seat or upper thigh of a pair of blue jeans, it can be reached, with a bit of maneuvering, to be patched on a sewing machine. I'll put the patch on the inside, and then just zig-zag stitch back and forth, up and down, until I've "quilted" the patch over the hole. But holes in the knee can't be fixed this way, unless you're willing to rip the leg seam and then sew it back up afterwards. Too much trouble - this way is easier and makes a long-lasting patch.
It's very handy to keep the legs from an old worn-out pair of blue jeans around as a patch supply (or pick up the biggest pair you can find at a thrift store). You can even match the amount of fading to the pants to be patched - taking the patch from down near the hem for darker pants, and using the faded upper thigh for lighter ones. First, cut a patch quite a bit bigger than the hole, rounding the corners.
Turn the pant leg inside out and pin the patch down so that both "wrong sides" are up. Hide your knot between patch and pant material and then, about a quarter-inch away from the edge, start stitching the patch down with a running stitch around the edge - four to five stitches to the inch. Continue around, and when you get back to your starting place, continue with another round, a quarter-inch to the inside. Two rounds is enough, but you can keep circling around until you run out of thread, and then fasten off.
Turn the pants leg right side out, and trim any long threads and end tufts from the hole. Keeping the pants leg as flat as possible to the patch (pin it if necessary), fold the ragged edges under and stitch with an overcast stitch, catching a bit of the patch material and then up through the edge of the fold. Tuck any loose threads under with the tip of your needle as you work your way around the rip. Fasten off, and you're done!