Step 1: Procure Pepper(s) and Knife
While you can use a paring knife, your fingers will be much closer to the peppers and will be more likely to pick up capsaicin. I'm using a 10inch chef's knife in these pictures.
Hot peppers have a nice, non-spicy external skin, so you want to hold it by the stem and the skin and avoid touching the seeds, cut surfaces, or internal flesh. The hotter the pepper the more relevant this separation becomes.
Step 2: Slice Pepper
Keep turning the pepper in order to place a flat side against the cutting board, then cut another slice off the side of the pepper. At the end of this process you should be holding a stem with the seeds still attached, and have a pile of pepper chunks sitting on your cutting board.
Step 3: Wipe Knife
Step 4: Flip and Slice Segments
Cut thin strips with the chef's knife, cutting through several layers at once in the pile. You will likely need to scrape stuck slices off the side of the knife; that's what the stem end is for. Whack off the seeded bits into the trash, then use your little handled scraper to shove any over-eager bits of pepper back onto the cutting board.
Step 5: Cross-cut
Again, you can use the stem end to wipe your knife clean as needed during the mincing process. The frequency will depend on your technique and the target size for your pepper chunks.
Step 6: Mince & Use
Now you've got a big pile of hot peppery goodness, and haven't exposed your fingers to the really dangerous parts. Use the knife to scrape your peppers into the necessary pot or bowl, then drop the cutting board safely into the dishwasher. Rinse the knife then wash thoroughly with soap and water, keeping your fingers clear until the knife is safely clean.
Wash your hands with soap to make sure any potential splatters are gone, then feel free to pick your nose or take out your contacts with impunity.