The transcript of the phone call between President Trump and President Zelinsky states that it "is not a verbatim transcript". What does this mean? How do we know they are not hiding something, or that this transcript was not faked?
Recent testimony by Lt. Col. Alexander S. Vindman, the top Ukraine expert on the National Security Council, has called the below answer into question. Testifying under oath to the House, Col. Vindman alleged that the released "transcript" was incomplete and omitted several explicit references to Biden and Burisma. Efforts to restore the full transcript were blocked by the decision to quickly move the transcript to the secure N.S.C. Intelligence Collaboration Environment, or NICE system:
Lt. Col. Alexander S. Vindman, the top Ukraine expert on the National Security Council, told House impeachment investigators on Tuesday that the White House transcript of a July call between President Trump and Ukraine’s president omitted crucial words and phrases, and that his attempts to include them failed, according to three people familiar with the testimony.
The omissions, Colonel Vindman said, included Mr. Trump’s assertion that there were recordings of former Vice President Joseph R. Biden Jr. discussing Ukraine corruption, and an explicit mention by Ukraine’s president, Volodymyr Zelensky, of Burisma Holdings, the energy company whose board employed Mr. Biden’s son Hunter.
Colonel Vindman ... told House impeachment investigators that he tried to change the reconstructed transcript made by the White House staff to reflect the omissions. But while some of his edits appeared to have been successful, he said, those two corrections were not made.
It is not clear why some of Colonel Vindman’s changes were not made, but the decision by a White House lawyer to quickly lock down the reconstructed transcript subverted the normal process of handling such documents, according to people familiar with the matter.
The rough transcript also contains ellipses at three points where Mr. Trump is speaking. Colonel Vindman told investigators that at the point of the transcript where the third set of ellipses appears, Mr. Trump said there were tapes of Mr. Biden.
The New York Times has posted an annotated copy of the document which they're calling "a reconstructed transcript". The transcript comes with the following disclaimer that explains the differences (emphasis is mine):
CAUTION: A Memorandum of a Telephone Conversation (TELCON) is not a verbatim transcript of a discussion. The text in this document records the notes and recollections of Situation Room Duty officers and NSC policy staff assigned to listen and memorialize the conversation in written form as the conversation takes place. A number of factors can affect the accuracy of the record, including poor telecommunications connections and variations in accent and/or interpretation, The word “inaudible” is used to indicate portions of a conversation that the notetaker was unable to hear.
They further clarify that:
Note: The words released by the White House recounting Mr. Trump’s conversation with Mr. Zelensky look like a transcript, but the document is marked, Memorandum of Telephone Conversation, and it warns that it is not a verbatim account. Instead, it was “developed with assistance from voice recognition software along with experts and note takers listening.”
Zelenskiy, who took office in May, spoke through a translator.
The New York Times also mentions a translator, though they only cite unnamed "officials":
An American official translated Mr. Zelensky’s statements into English, officials said. The document included three ellipses indicating that part of Mr. Trump’s comments may be missing, though it is unclear how much was left out. Administration officials said the ellipses indicated when Mr. Trump trailed off or was inaudible.
This could explain why the transcript appears shorter than one might expect from the length of the phone call (30 minutes).
As for the question of how we know they're not hiding something: we just have to trust that if The White House is hiding anything, the House's investigation will uncover it and make it public, since revealing that would be very much in their interest. To quote Federalist 51: "Ambition must be made to counteract ambition"
Divibisan's answer above answers your title question. The Washington Post attempts to expand on that by way of a former senior director of the White House Situation Room explanation of the process that is (or was) used to produce transcripts (referred to as a TELCON).
As to your question "are they hiding or faking something", this (from the same article):
former White House staffers said that the Trump administration, in a departure from prior presidencies, has been more willing to edit the telephone conversation memos to remove errors or insensitive remarks Trump has made, apparently in an effort to avoid political heat or embarrassment.
“Don’t rely on whatever transcript is released,” said a former staffer, who spoke on the condition of anonymity to comment candidly. “Even if it’s unredacted; those transcripts are heavily edited by political leadership at NSC. I’ve seen substance deleted from these call ‘transcripts’ to delete either superfluous details or more substance.”
So, the answer to your "hiding or faking" question is not able to be answered definitively.
BTW, I suspect that the "voice recognition software" referred is actually speech recognition software that is used in many courtrooms today, for example: Dragon Legal Edition