Say a publisher or other organization creates "a new translation" of the Bible: What's the source text? Are they experts in ancient Aramaic? What exactly is the text being translated from in modern times?
The Hebrew Bible is primarily in Biblical Hebrew (the term given to the Semitic language that the Bible was written in from which modern Hebrew descends) with some Aramaic in various places (Ezra 4:8-6:18; 7:12-26; Jeremiah 10:11; Daniel 2:46-7:28; and two words in Genesis 31:47).
The New Testament is in Koine (common) 1st-century Greek. Koine Greek descends mainly from Attic Greek, with some input from other dialects. There are also some Aramaic words and expressions that are transliterated into Greek.
Concerning source texts, there are tons of copies of manuscripts and it is disputed which is the original (and even which language is the original). Several critical editions of the Hebrew Bible and New Testament have been produced which are used today by scholars for translation. The Hebrew Bible primarily relies on the Masoretic Text. As more manuscripts are discovered, these critical editions are updated to reflect current scholarly findings. Previous generations classified New Testament manuscripts based on text-types such as "Alexandrian," "Western," "Byzantine," and "Caesarean." However, modern scholars have proposed alternate approaches to manuscript evidence such as the Coherence-Based Genealogical Method.
Also important to translators are previous translations into other languages (such as the Latin Vulgate and the Greek Septuagint) which reveal what manuscripts older translators had access to which may not be available today. Also, quotes from the Bible by ancient authors in other works are important as it shows what texts they used. For instance, the infamous Comma Johanneum (1 John 5:7-8) was never quoted by early Christian Church fathers in arguments concerning Trinitarian heresies, which supports the claim that it was a later addition to the text.
The source texts for the NT include various Greek manuscripts and sometimes the Latin Vulgate.
The source texts for the OT include the Masoretic text (Aleppo Codex, Leningrad Codex), as well as the Latin Vulgate, Greek Septuagint, and Dead Sea Scrolls.
Translators of new English translations often use some or all of those source texts when producing a new English translation.
Hardly any Aramaic source texts are used, unless you include the Aramaic scriptures of Daniel and Ezra, but again, those are considered to be part of the Masoretic text. Other Aramaic source texts would be the targumim, but they would not be considered a greater witness than the Masoretic when producing an English translation of the Old Testament/ Hebrew Tanakh.
For example, here is an excerpt from the Lockman Foundation website describing the source texts used for the translation known as the "New American Standard Bible" (NASB):