道, dào: Way, road, path. In Daoism the Dao is the Way of the universe, the cosmic law that precedes the Gods and existence itself, and which both birthed the universe and determines how the entire universe functions.
I have simply decided to translate Dao as Way, capitalised as a proper noun. The one exception is in chapter 1 itself, where I translate the second instance of 道 as mapped. A straight rendition of the first line (道可道，非常道) in English would be something like "The Way that can be Way'd is not the constant Way." Dao can be used as a verb in a variety of manners, typically in English we see something like "Spoken," or "Uttered." These do have precedent in Chinese texts, but I believe the prominence here is due to how naturally the verb form comes off in English here. I chose mapped because I think it gets across the spatial, doctrinal, and epistemological metaphor of the line all in one word, something few translations do, while being equally as natural.
德, dé: Virtue, character, integrity, favour. In Daoism De refers to the specific characteristics conferred upon someone who aligns themselves properly with the Dao, a sort of spiritual potency that can only be gained by proper alignment with nature.
De is typically translated as "Virtue," which works perfectly across Classical Chinese as a whole, but proves somewhat misleading in the Dao De Jing. The moral aspect that the word is often associated with doesn't show itself here. I chose the word "Character," as awkward as it can be, since it's the most natural translation of the word into English.
常, cháng: constant, typical, often, permanence, pattern. In Daoism Chang is the particular quality in the universe, and in things within it, that never changes. It is the reoccurring pattern of a thing, which never leaves it from birth to death, and of the universe from beginning to end, associated with the Dao's relationship with that particular thing, or with everything.
Chang is seemingly a simple word to translate, a direct temporal modifier that just indicates something repeats, yet it's the most deceptively difficult word to translate in the entire text. One option is to simply say "Constancy," which is how one might use it as a proper noun, if you were say writing a dictionary of Daoist terms. Fitting for a text like the Yìjīng, but insufficient for a 81 verses of poetry. Here I have translated it contextually, as everlasting, constant, or nature.
Everlasting and constant are self explanatory, nature requires explanation. The problem is that to capture what Chang is in English is nigh impossible in a single word without compromise, certainly nothing that would let a native reader parse the meaning intuitively. Here I went with nature for I believe it is the only word a native reader would be able to read and instantly pick up the connotation of. Nature is one of the most semantically wide words in English, capturing innate disposition, connotations of the natural world, spontaneity, and a host of other ideas. In this particular text, it's the most natural way to reckon both with Chang and with 自然 (zìrán). I lament that erd is too antiquated to be employed here.
無為. wúwéi: Literally no-action, not-acting, without-acting. In Daoism a term for spontaneous unforced action, not not-acting but not "acting."
I take a somewhat unusual approach with wu-wei. Rather than translating it universally as "no acting," or "acting without acting," as is typical, I decide to translate it contextually, tweaking the phrasing to make it read naturally and meaningfully in every occurrence, while still staying firmly within the bounds of everything wei, and acting, semantically implies. I take the semantic hinge here, which makes the phrase work in the first place, to be acting not as the literal physical act of acting, but the psychological process of acting that one does when they're cast as a character in a play, meeting their girlfriend's parents, or playing a tabletop game—putting up a front, so-to-speak—hence the translations, "act without 'acting'" "play no role," "play the part."