Put something flat and rigid under the patch area.
Rig something up to hold the patch area material flat and somewhat tight.
Clean area under the patch with alcohol a bit larger than the patch.
Cut patches with rounded corners, any square corners will have a tendency to wanna lift.
I'll echo what others have said, packer58 covered the specifics, tenacious tape is great stuff! I've patched my down coat, ember holes in my tipi and other items and it lasts for years. Sometimes I will warm the area I'm patching with my wife's hair dryer before applying the patch to encourage adhesion and then apply weight with the palm of my hand until it cools off.
I've only ever done square/rectangle patches of Tenacious Tape and they hold really well, even through the wash. I have replaced some after years but I bet rounding the corners would solve that problem. The patch would probably outlive the garment itself.
I've used noso patches and tenacious tape. I prefer using noso patches when I can do the repair at the house and use tenacious tape in the field. The noso patches seem to last longer for me. I've got a pair of Kuiu guide pants with a noso square and it's lasted over 5 years the only wear it has shown is the color is faded. My Sitka Jacket has tenacious tape and has lasted a few years, but is starting to break away and needs replaced. Both are great products.
I've used Tenacious tape on hunting pants, down jackets, and even on my canvas wall tent, and it just flat out works. I tore my pants crossing a barbed wire fence several years ago now in the shape of an "L". I cut a piece of tape to match it and put it on, and it's still holding even through many wash and dry cycles. And I have to really look to even identify which pants have that tape on them.