Puer sursum in arborem ascendit, ut nidum videat.

Because puer is in the nominative singular, which is the case normally used for the subject.

• puer = boy
• its ending shows it is the subject, even without a separate word for he

So Latin tells you who is doing the action by the form of the noun, not mainly by word order.

Yes, ascendit already means climbs or goes up.
sursum is an adverb meaning upward or up.

So sursum adds emphasis or vividness, much like English sometimes says climb up even though climb already suggests upward movement.

Latin often uses this kind of combination naturally:

• ascendit = he climbs
• sursum ascendit = he climbs up / goes upward

Because in changes meaning depending on the case that follows it.

• in + accusative = motion into or onto something
• in + ablative = location in or on something

Here the boy is moving into or up onto the tree, so Latin uses in arborem.

Compare:

• in arborem = into / onto the tree
• in arbore = in the tree

Not every accusative is a direct object.
Here arborem is accusative because the preposition in takes the accusative when it shows motion toward something.

So:

• nidum is accusative as the direct object of videat
• arborem is accusative because of in with motion

They are both accusative, but for different reasons.

Formally, ascendit can be either:

• he climbs / is climbing — present
• he climbed / has climbed — perfect

This is a common point of confusion, because the forms are identical.

In this sentence, many learners will take ascendit as present, especially because the purpose clause has videat, a present subjunctive. If the sentence were clearly past in classical prose, you would often expect videret instead.

So context is what tells you how to translate ascendit.

Because ut introduces a purpose clause here, and purpose clauses use the subjunctive.

So:

• videt = he sees
• videat = he may see / so that he may see

That is why ut nidum videat means something like:

• so that he may see the nest
• in order to see the nest

Here ut means so that or in order that.

It introduces the reason or purpose for the action in the main clause:

• main action: Puer sursum in arborem ascendit
• purpose: ut nidum videat

So the idea is that the boy climbs up into the tree for the purpose of seeing the nest.

Because the verb ending already shows the subject.

videat means he may see
ascendit means he climbs / he climbed

In Latin, subject pronouns such as he, she, or they are often omitted unless they are needed for emphasis or contrast.

So Latin does not need to say he separately here.

Latin word order is much more flexible than English word order.

English depends heavily on order:

• The boy sees the nest

Latin depends more on endings, so the order can move around for style, emphasis, or rhythm.

Here:

• nidum videat is a very normal Latin order
• the verb often comes at the end of its clause

So nidum videat feels natural in Latin even though English would normally put see earlier.

nidum is accusative singular.

It is accusative because it is the direct object of videat:

• the boy may see what?
• the nest

So:

• videat = may see
• nidum = the thing seen

The comma is there to separate the main clause from the purpose clause:

• Puer sursum in arborem ascendit
• ut nidum videat

This helps modern readers. But punctuation in Latin texts is much less fundamental than in English, and ancient Latin writing did not use punctuation in the same way modern editions do.

So the comma is helpful, but it is not the main thing that tells you the grammar. The grammar is shown by ut and the subjunctive videat.