La segretaria mi fa una fotocopia del passaporto e me ne prepara anche una seconda.

In Italian, a specific person who is the subject of the sentence usually takes an article. So la segretaria means the secretary.

Using segretaria without an article would sound unusual in a normal sentence like this, unless it were a label, headline, or some very special style.

Mi is an indirect object pronoun meaning to me or for me.

So:

• La segretaria mi fa una fotocopia
  = The secretary makes me / for me a photocopy

In natural English, for me is often the best way to understand it here.

Because fare una fotocopia is a very common Italian expression meaning to make a photocopy.

So:

• fare una fotocopia = to make a photocopy

This is more idiomatic than trying to translate word-for-word from English.

Del is the contraction of di + il.

• di = of
• il passaporto = the passport
• del passaporto = of the passport

After fotocopia, Italian normally uses di to say what is being copied:

• una fotocopia del passaporto = a photocopy of the passport

Because when mi, ti, ci, vi combine with another pronoun such as ne, they change form:

• mi → me
• ti → te
• ci → ce
• vi → ve

So standard Italian says:

• me ne
• te ne
• ce ne
• ve ne

That is why me ne prepara is correct, not mi ne prepara.

Ne refers back to something already mentioned with di, here del passaporto.

So in this sentence, ne basically means of it or from it, and in natural English the whole phrase becomes:

• me ne prepara anche una seconda
  = she also prepares a second copy of it for me

So ne is what links the second copy back to the passport already mentioned.

Because una seconda by itself only means a second one.
Ne tells you a second one of that / of it.

Without ne, the connection to del passaporto would be missing or much less clear.

So:

• me ne prepara anche una seconda = she also prepares a second one of it for me

That is the natural and complete structure.

Una seconda means a second one.

The noun fotocopia is not repeated, but it is understood:

• una seconda (fotocopia)

Because fotocopia is feminine, the phrase is feminine too:

• una seconda

This is a very common kind of omission in Italian when the noun is already clear from context.

They are similar, but not identical.

• una seconda = a second one
  This emphasizes number: the copy will be number two.
• un'altra = another one
  This is a little less explicit about numbering.

In this sentence, una seconda makes it especially clear that there is a first photocopy and then a second one.

Both verbs work, but they are doing slightly different jobs stylistically.

• fa una fotocopia = makes a photocopy
• prepara una seconda = prepares a second one

Here prepara can suggest gets ready / produces / prepares the additional copy. It also helps avoid repeating fa twice.

So the sentence sounds a bit more natural and less repetitive.

Because these are unstressed object pronouns, often called clitics, and in normal Italian they usually go before a conjugated verb.

So:

• mi fa
• me ne prepara

That is the standard order.

Also, when there are two pronouns, their order is fixed here:

• me
  • ne
    • prepara

You cannot rearrange them freely.

Anche means also, too, or as well.

Here it shows that, in addition to making one photocopy, the secretary prepares a second one too:

• first copy: mi fa una fotocopia del passaporto
• additional copy: me ne prepara anche una seconda

So anche highlights the extra action.

Grammatically, that is roughly how the Italian is built, but it is not how natural English works.

A more useful way to understand the structure is:

• me = for me
• ne = of it
• una seconda = a second one

So the natural English meaning is:

• she also prepares a second copy of it for me

For learners, it often helps to see the literal pieces, but then switch back to a normal English translation.