What tapping does

Tapping recuts the threads inside the t-nut so a bolt can tighten smoothly again. It's a metal cutting operation performed above a room full of people, so the PPE and the cleanup aren't extras, they're part of the job. Cut as close to the original thread lines as you can. A second set of threads alongside the first weakens the t-nut for no reason.

New t-nuts too

Brand new t-nuts sometimes need tapping before first use, to clear manufacturing burrs along with paint, wood, concrete and general construction debris.

The sequence

Gear up. Taps physically cut metal, and metal shavings are the output. Face shield, or goggles that actually seal to your face, plus whatever else your facility requires.
Get out from under it. Don't tap above your head unless it's genuinely unavoidable. Shavings fall, and they land in eyes and faces.
Set up something to capture debris. A bucket, tarp, or collection bin under the work. Magnets and vacuums can be helpful too.
Find the original threads. Start the tap with the existing threads.
Clean the t-nut out. Blow it out and run a magnet through it before the new bolt goes in, so you don't weld fresh shavings into a brand new jam.
Clean up around you. Shavings land in nearby holds and in the flooring. A metal thread sitting in a jug can end up in somebody's hand.

Tap types

Manual taps run by hand, speed taps run off a drill. Either way the PPE and the cleanup are the same. Seek professional instruction, practice with taps, and use them only in appropriate situations and positions.