For a long time this seemed to me like an esoteric and scary task, but when I had to do it, I discovered that it is not difficult at all. It requires a bit of time, a bit of fiddling, and a tap & die set, but is well within anyone's ability who has full use of their hands. I do not even own this tap & die set, I borrowed it from my cousin! You may have a cousin with a tap & die set too. Many people do.
Cutting oil is available at any hardware store. You can if necessary get away without this but I recommend it. We found, having tried it, that lubrication did two things: it made starting the tap a lot easier, and it made the threads a little tighter so that the screw was not quite as loose in the hole. In fact in a couple cases we needed to use a wrench to get the screw all the way tight! This is not a very big deal either way but I suspect that the tighter screw will last longer.
Step 1: What Size?
In our case we had 3/8" screws, and therefore needed to drill holes of 5/16". This information is helpfully printed on the tap itself! The thread gauge for our screw is 16 threads per inch. The tap set had a handy little tool for measuring this, but it is also easily possible to count threads next to a ruler.
Step 2: Preparation
Clamp your metal solidly to something that won't move, or otherwise fix it in place. Run a light coating of oil over the edges of the tap screws. You're ready to go.
Step 3: Twist
I found that a good starting technique was to hold the handle close to my body, and turn with my hips, keeping my hands in the same relation to my body the whole time. I kept my eye on the end of the tap where it was held in the handle, and concentrated on that not moving sideways. After the tap has set it was fine to ease off on this and turn by hand.
The tap works by scraping a spiral groove on the inside of the hole. The metal displaced from the groove in the hole is pulled into the grooves on the tap. You're doing this by hand, and it gets hard to cut the metal pretty quickly -- after about a quarter turn the tap gets very stiff. This is because the piece of metal already scraped out is too big now. To cut it off so it can drop out of the way, reverse the tap direction for a quarter or even a half turn. You will hear and feel the other side of the tap screw edge knocking off the metal scraping.
Keep doing this until the tap is all the way through, and turns freely. The bottom 1/4" or so of the tap, called the chamfer, should be entirely sticking out. Then simply unscrew the tap out of the hole again. Don't forget to clean off the oil and metal shavings!