Vi ĝuste pendigis la afiŝon.

Vi means you, and it can be:

• singular: you
• plural: you all / you guys
• formal: polite you

Esperanto normally uses vi for all of these. There is an old singular informal form ci, but it is very rare in normal modern Esperanto.

Here ĝuste means something like correctly, properly, or accurately.

Depending on context, ĝuste can also mean exactly. So the exact English choice depends on what meaning was intended. In this sentence, it most naturally describes how the action was done: you hung the poster the right way.

Because pendi and pendigi are different verbs.

• pendi = to hang, to be hanging
  This is usually intransitive: the thing is already hanging.
• pendigi = to make something hang, to hang something up
  This is transitive: someone causes an object to hang.

So:

• La afiŝo pendis sur la muro. = The poster was hanging on the wall.
• Vi pendigis la afiŝon. = You hung up the poster.

This is a very common Esperanto pattern:
-ig- adds the idea cause/make.

-ig- is a suffix that means to cause, to make, or to turn into a transitive action.

So:

• pendi = to hang, to be hanging
• pendigi = to cause to hang, to hang up

Literally, pendigis is something like caused to hang.

This is one of the most useful word-building tools in Esperanto.

-is is the past-tense verb ending in Esperanto.

So:

• pendigas = hangs / is hanging up
• pendigis = hung up
• pendigos = will hang up

Esperanto verbs always show tense with their endings, so you do not need an extra word like English did or a change like hang/hung.

The -n shows the direct object.

In this sentence, la afiŝon is the thing being hung up, so it takes the accusative ending -n.

• La afiŝo = the poster
• la afiŝon = the poster, as the direct object

A native English speaker can think of this as marking what received the action.

La is the definite article, meaning the.

So:

• afiŝo = a poster / poster
• la afiŝo = the poster

Esperanto has only one article, la, and it does not change for gender, number, or case. Even when the noun takes -n, the article stays the same:

• la afiŝo
• la afiŝon

Yes. Esperanto word order is fairly flexible because endings show the grammar.

This sentence could also appear as:

• Vi pendigis la afiŝon ĝuste.
• Ĝuste vi pendigis la afiŝon.
• La afiŝon vi ĝuste pendigis.

But the emphasis changes.

The original Vi ĝuste pendigis la afiŝon most naturally means that the action of hanging the poster was done correctly.

For example:

• Vi ĝuste pendigis la afiŝon. = You hung the poster correctly.
• Ĝuste vi pendigis la afiŝon. = It was specifically you who hung the poster.
• Vi pendigis ĝuste la afiŝon. = It was specifically the poster that you hung.

So word order can shift meaning slightly through emphasis, even though the basic grammar still works.

• ĝ is pronounced like the j in judge
• ŝ is pronounced like sh in shoe

So:

• ĝuste sounds roughly like JOOS-teh
• afiŝon sounds roughly like ah-FEE-shon

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

• ĜUS-te
• a-FI-ŝon
• pen-DI-gis

Yes. Esperanto often builds words from pieces very regularly.

pendigis can be broken down as:

• pend- = hang
• -ig- = cause, make
• -is = past tense

So the structure is very transparent:
pend-ig-is = caused to hang in the past.

This kind of word-building is one of the most characteristic features of Esperanto.