Mi ne kredas tiun mensogon.

Because tiun mensogon is the direct object of kredas.

In Esperanto, the direct object usually takes the accusative ending -n. Words that go together also agree with each other, so:

• tiu mensogo = that lie
• tiun mensogon = that lie (as a direct object)

Here, the speaker is not believing that lie, so that lie is the thing being acted on by the verb kredas.

Tiu is the basic form meaning that one / that.

When it modifies a noun and the whole noun phrase is a direct object, it changes to tiun to match the accusative:

• tiu mensogo = that lie
• tiun mensogon = that lie (object form)

So tiun is not a different word; it is just tiu with the object ending -n.

For the same reason: mensogo is the noun, and as a direct object it takes -n.

• mensogo = a lie / lie
• mensogon = a lie / lie as the direct object

Since the sentence is about not believing the lie, mensogon is the object of kredas.

Ne means not. It negates what follows, and in normal sentences it usually comes before the verb:

• Mi kredas = I believe
• Mi ne kredas = I do not believe

So Mi ne kredas tiun mensogon means I do not believe that lie.

Placing ne before the verb is the most normal and straightforward word order here.

Esperanto does not use a helper verb like English do for negation.

English needs:

• I do not believe

Esperanto simply uses:

• Mi ne kredas

So ne handles the negation by itself. There is no extra verb needed.

Because -as is the present-tense ending in Esperanto.

The verb is kredi = to believe. Its forms include:

• kredi = to believe
• kredas = believe / am believing
• kredis = believed
• kredos = will believe

So Mi ne kredas means I do not believe or I am not believing.

Yes. Kredi can mean to believe something, so it can take a direct object:

• Mi kredas tion. = I believe that.
• Mi ne kredas tiun mensogon. = I do not believe that lie.

A useful contrast is:

• kredi ion = believe something
• kredi al iu = believe someone

So:

• Mi kredas tiun rakonton. = I believe that story.
• Mi kredas al vi. = I believe you.

In your sentence, the speaker is believing or not believing the lie itself, so the direct object is correct.

Because tiu and tia mean different things.

• tiu = that specific one
• tia = that kind of / such a

So:

• tiun mensogon = that lie
• tian mensogon = that kind of lie / such a lie

In your sentence, the meaning is about one specific lie, so tiun mensogon is the natural choice.

Because tiu already makes the noun definite and specific.

Esperanto often does not use la together with demonstratives like tiu. Compare:

• la mensogo = the lie
• tiu mensogo = that lie

Using tiu already points to a particular lie, so la is unnecessary.

The normal word order is:

• Mi ne kredas tiun mensogon.

Because Esperanto marks the direct object with -n, the word order can be changed more freely than in English, especially for emphasis. For example:

• Tiun mensogon mi ne kredas.

This still means I do not believe that lie, but it emphasizes that lie.

Even so, the version you have is the most neutral and standard order.

A rough pronunciation guide is:

Mee neh KREH-dahs TEE-oon men-SO-gon

A few details:

• mi = mee
• ne = neh
• kredas = KREH-dahs
• tiun is usually said like TEE-oon
• mensogon = men-SO-gon

Also remember that Esperanto stress normally falls on the second-to-last syllable:

• kredas
• tiun
• mensogon

Not exactly. Kredi means believe, not really trust.

So Mi ne kredas tiun mensogon clearly means I do not believe that lie.

If you want to talk about trusting a person, Esperanto usually uses other expressions, such as fidi al iu for trust someone. So this sentence is specifically about not accepting the lie as true.