Fumus sursum ex foco ascendit, et infans eum miratur.

Latin word order is much freer than English word order because the endings on words show their grammatical roles.

• Fumus is the subject because it is nominative singular.
• ascendit is the verb.
• ex foco tells where the smoke comes from.
• sursum adds the idea upward.

So Latin does not need to keep a rigid subject–verb–object order the way English usually does. The sentence could be rearranged in other ways and still mean basically the same thing, though the emphasis might change.

Sursum is an adverb. It means up, upward, or upwards.

It modifies the verb ascendit, telling us how or in what direction the smoke rises.

So:

• ascendit = rises / goes up
• sursum ascendit = rises upward

In English this can sound a little repetitive, and it can be slightly emphatic in Latin too.

Ex is a preposition that takes the ablative case, so foco is ablative singular.

• focus = hearth, fireplace
• ex foco = out of the hearth / from the hearth

This is a very common Latin pattern:

• ex
  • ablative = out of / from
• in
  • ablative = in / on in some contexts
• cum
  • ablative = with

So foco ends in -o because it is the ablative singular of a second-declension masculine noun.

Latin present tense often covers both ideas that English separates:

• simple present: rises
• present progressive: is rising

So ascendit can naturally mean either, depending on context.

Formally, ascendit is:

• 3rd person singular
• present tense
• active voice

Because the subject is fumus (smoke), the verb means it rises or the smoke rises.

In Latin, the verb ending already shows the person and number, so a subject pronoun is often unnecessary.

• ascendit = he/she/it rises

The ending -it tells you the verb is 3rd person singular, so Latin does not need to add a separate word for it.

Then fumus is stated explicitly as the subject, so everything is clear.

Eum is the accusative singular masculine form of the pronoun meaning him/it.

Here it refers back to fumus. Since fumus is a masculine noun, the pronoun must also be masculine:

• fumus = masculine
• direct object pronoun referring to it = eum

Even though English uses it for smoke, Latin matches the grammatical gender of the noun, not natural gender.

Because it is the direct object of miratur.

In infans eum miratur:

• infans = the subject
• miratur = wonders at / admires
• eum = the thing being admired or looked at with wonder

Direct objects normally go in the accusative case in Latin, so eum is accusative singular masculine.

Because miror, mirari is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

So:

• miratur looks passive in form
• but means he/she/it admires, wonders at, or looks at with wonder

This is a very important Latin pattern. Some common deponent verbs are:

• miror = admire, wonder at
• loquor = speak
• sequor = follow

So infans eum miratur does not mean the child is admired by him/it. It means the child admires it.

Infans here is nominative singular, the subject of miratur.

It belongs to the third declension, where nominative forms are often less predictable than in the first or second declensions. So unlike a noun such as puella or servus, the nominative singular does not always have a very clear standard ending.

You recognize its role mainly from:

• its form in the sentence
• the fact that it agrees as the subject with miratur
• the meaning of the sentence

It can mean either, depending on context.

For miror, the core idea is something like:

• to marvel at
• to look at with wonder
• to admire

In this sentence, a child looking at rising smoke probably suggests wonders at it or looks at it in amazement, though admires it is also possible depending on the translation style.

Latin has no articles equivalent to English the and a/an.

So:

• fumus can mean smoke, the smoke, or sometimes a smoke, depending on context
• focus can mean hearth or the hearth
• infans can mean child, the child, or an infant/child

English has to choose an article when translating, but Latin usually leaves that to context.

Yes. Latin word order is flexible, so several arrangements are possible, for example:

• et infans eum miratur
• et eum infans miratur
• et infans miratur eum

All are grammatically possible. The chosen order may affect emphasis or style, but the endings still show the relationships:

• infans = subject
• eum = object
• miratur = verb

The sentence as given is a straightforward, readable order for a learner.