The word 道 (dào) has several different meanings. One of these is "road/path/way"; another is "speak/utter". This is where Wikisource's translation comes from: the first 道 means "road", and the second means "speak".
Chinese also has much less verbal morphology than English does. Where English uses the whole verbal phrase "is able to be spoken", Chinese just uses two words, 可 ("able to") and 道 ("speak"). The time of the action isn't relevant (it's a "gnomic" sentence), and the voice of the verb is clear from context: it's not a road speaking, it's a road that's able to be spoken/explained. Similarly, Chinese doesn't generally use anything equivalent to English "a" or "the", but English requires them, so the translator adds them in.
A big part of translation is knowing what needs to be stated in each language. This translation…
Dao permits Dao, negating a permanent Dao
…isn't a very good one, in my opinion, because it's ignoring the context. Sure, 道可道 could mean "speaking permits a road". But contextually, that doesn't make much sense at all. Out of the hundreds of possible interpretations, adding tense and voice to the verb (because English requires that), "the path which is able to be spoken aloud" seems like the most reasonable one.
For some more examples, here are how some professional translators handled this first sentence.
The Dao that can be trodden is not the enduring and unchanging Dao. The name that can be named is not the enduring and unchanging name. (Legge)
The Reason that can be reasoned is not the eternal Reason. The name that can be named is not the eternal Name. (Susuki)
The Dao that can be understood cannot be the primal, or cosmic, Dao, just as an idea that can be expressed in words cannot be the infinite idea. (Goddard)
Note that all of them supplied many, many words that don't correspond to anything in the Chinese sentence! English is a somewhat verbose language, in that it needs to use a lot more words, and specify a lot more details, than Chinese does. So the translator has to add those in to get good, understandable English.