One nice thing about this project is that you can be as fussy or as laid back about your inscription as you want to be. The plant label is, after all, for your benefit: So you are the final arbiter in deciding what it should look like and how much time to spend on making it. If you don't feel like being fussy, this project can go very quickly.
Your first decision between "fussy" and "laid back" comes in using the wood burning tool for lettering. If you go the fussy route, you can write out the letters of the plant name first in pencil, so that you have a guide to go by when using the wood burning tool. If you wish to get really fancy, you can even draw out lines (like the lines on lined paper) on the plastic pot, creating perfect rows for your letters to reside in (you can erase the lines after the incisions are complete).
Saving time was important to me, so I went the laid back route, inscribing the letters free-hand with the wood burning tool. But at the very least, have the original plant label that the plant came with handy if you're unsure that you can spell its name right from memory.
To begin, plug the wood burning tool into an outlet, so that it heats up. Next, gently hold the tip of the wood burning tool up against the plastic pot, where you wish to inscribe the letters. I say "gently" because the plastic will begin melting immediately upon contact, and you do not want to burn a hole clean through the container! Your goal is to remove a small amount of plastic, so as to leave behind a shallow yet visible incision.
There's a choice in how to proceed next, as discussed in Step 4....