The teaching you quote itself explains the derivation of טוב as "preparing" by analogy to הטבת הנרות (preparing the candles).
The classic example is “hatavat haneirot,” preparing the wicks of the candles/lamps in the Temple to be lit by the Kohen.
The expression appears, for instance, in Exodus 30:7 (בְּהֵיטִיבוֹ אֶת-הַנֵּרֹת).
The derivation of רע as unstable, also quoted on the linked website, isn't spelled out, but "broken" is the clearest explanation of certain verses (e.g. Isaiah 8:9: רֹעוּ עַמִּים וָחֹתּוּ), and the contrast with this meaning of רע might be another reason to understand טוב as an opposite meaning.
I looked through the original commentary (here) and didn't find this derivation of the word. I'm guessing that this derivation of טוב (given in parentheses) might have been the addition of the author of the article. The Maharal seems to be giving more of a metaphysical proof that any lasting thing in existence contains good ("כי אין לדבר קיום רק מצד הטוב"), rather than a linguistic proof.