Step 1: Materials Needed
Just lay the pants over the damaged area, and cut around it. I like to leave about 2" of material past the edges of the hole on all sides. This allows some extra for the hem, plus it makes sure that when I sew it down, I'm sewing into good material, and not part that's about to fall apart. Next, make sure you have rounded corners. If you leave a sharp corner, it will tend to get caught on things, no matter how well you sew it down.
The other three things you will need are curved needles, ultra-heavy-duty thread, and some foam (I used a mattress topper). You will also need a sewing machine and regular thread. Oh, and you'll need a truck with a hole in the seat ;-)
Step 2: Hem the Patch
Hemming is basically just folding over the edge and sewing it down. I like to use a zigzag stitch over the edge of the fabric, but you can hem with a straight stitch. Since it will be inside the bench, it's never going to fray.
Hemming around a curved corner is a little harder than ordinary hemming, especially with denim. Basically, when the folded fabric doesn't want to sit where it needs to, you lift the presser foot with the needle sunken into the fabric, but not in the hem (see second image). Then you re-fold the fabric hem so that it is where it should be, and drop the presser foot. This will cause a small 'gather', but you can just sew right over this. A rounded corner should have 3 or 4 of these.
After you've hemmed the entire patch, be sure to trim off all of the loose tails on both sides of the patch.
Step 3: Stuff the Hole
Cut small pieces and stuff them into the hole. You want to have it tightly packed at the bottom of the hole, but you don't want it bulging out at the top. The more it bulges at the top, the the tighter you'll need to sew the patch down. You also want to be sure that there aren't any sudden edges in your foam; I tapered the top layer's edge with scissors so that it was a smooth transition from the original foam to the added foam.
I actually spent a lot of time getting this 'just right'; once you've sewn down the patch, there's no way to fix the foam. I placed the patch over it, then ran my hand over it to make sure it was smooth, without any lumps. Take your time on this step.
Step 4: Sew Down the Patch
First, you want to prepare your needle & thread. I like to use a longer piece of thread so that I have to tie it off fewer times, but for first-timers, you may want a shorter piece. I would recommend cutting off about 5' of thread. Thread your needle onto it, then tie the two ends together (see the first image). Hand sewing is always done with the thread doubled over. You'll want to tie about 3 knots over the top of each other, making a very large knot. This is to prevent it from slipping through the fabric. Leave a half in or so after the knot; this is called the thread tail.
Next, you will need to start off the thread. I started from underneath the original fabric, so that the thread tail won't be visible. After starting it, you'll need to lay the patch onto the seat and get it situated how it will be. Start at the top, and work your way to the bottom. If there are any mistakes, they'll catch up to you at the end (you'll have a gather where there shouldn't be one), and it's better to have them out of view.
If you want to patch to last well, you'll want to make sure to have your stitches close together, but with a hemmed patch and extra-strong thread, they don't have to be closer than 1/5" or so.
Step 5: All Done!
After I was completely finished, I decided to go back and use some spray on fabric dye from Rust-oleum, called 'Fabric & Vinyl Flat'. It darkened it up a lot; perhaps too much.