The New Testament was originally written in Greek. Nowadays many translators in formal training programs take courses in order to understand the Greek text. However, not many know Greek well enough to translate solely from the Greek text. Thankfully, there are a number of helps available to Bible translators today which can aid them in understanding the source text.
Thirty years ago, a Bible translator needed a variety of books: commentaries, several versions of the Bible, dictionaries of biblical terms, maps for the historical settings, etc. Today, a translator has all of these tools available to them on computer software! Using a program called Paratext (developed jointly by the Bible Society and SIL), the translator can open six or more Bible versions at once to compare how a particular passage is rendered. While they are translating, they can type the local language version right into the same program. Have a question about what something means? Just click on a dictionary or commentary to research it further.
Another program, called Translator’s Workplace, offers additional help in understanding the passage. Still another program called BART gives a word-by-word literal translation of the Greek text. And the good part is that all these programs link and move through a passage together! Things sure have changed since the translator’s work table was littered with a dozen books, all blowing in the breeze!
In many situations, translators also consult national or regional language texts such as Swahili, French or Filipino. Since churches may have already been using these, it is good to consult them when translating, and try to match as much of the style as possible.
So, to answer the question of which source text is used: many versions are examined in order to arrive at the original meaning of a passage and to provide possible phrasing options. Many additional helps are consulted as well.