Step 1: 1. Measure Your Threads.
We want to figure out the thread measurement that we're going to recreate on our new part, and the way to do that is to try fitting different gauges until one matches perfectly. You will feel this instantly, and there won't be any question if it's the correct match- it's a powerful feeling of rightness, like a double rainbow over an ice cream cone of satisfaction. With sprinkles.
There are metric and english thread sizes, and if you can't find teeth that match your threads on one gauge, you're probably on the other measurement system. Metric threads are measured from peak to peak, if you look at them sideways. English threads are measured by number of peaks or threads per inch.
The gauge will have the thread information printed on it, allowing us to select the proper tap for the job.
Step 2: 2. Set Up Your Tap.
Every Tap and Die kit will come with a handle for holding taps and a handle for holding dies. The photo demonstrates the set up.
Step 3: 3. Set Up Your Work Space
So, to avoid this: think carefully about your set up. You want to maintain even physical pressure at 90 degrees to the tap. It depends on the shape of your parts, but in this case it was easiest to vice up the nice square tap handle and turn the knob by hand.
Step 4: 4. EnThread!
Every few turns, use a little tap oil or coolant from the machine shop. This is double extra important if you aren't changing thread sizes, but are tapping a drilled hole.
You need to clear the chips out of the teeth of the tap as you go, or it won't be able to cut and may shear off. I turn backwards halfway for every full turn, this is more than enough. Be very gentle when changing directions: you want to do everything you can to continue the threads you've started to set, and you can easily ruin them by too much wobbling or forcing.
Stay zen and work your way down: the further you get the more chips you'll have to clear. The bonus of this upside down setup is the chips want to fall out, but if you're going the other way they'll want to pack down into the threads you're trying to make.
Don't forget you will hit bottom at some point, in this case.
NEVER FORCE! If it feels wrong, it probably is.