Лиса быстро убежала, когда увидела белку на дереве.

Because both verbs are in the past tense, and in Russian the past tense agrees with the subject in gender and number.

The subject is лиса, which is feminine singular, so the verbs are also feminine singular:

• убежал = he ran away

• убежала = she ran away

• увидел = he saw
• увидела = she saw

If the subject were masculine, you would use убежал and увидел instead.

Russian often omits subject pronouns when the subject is already clear from context.

In this sentence, the subject is already лиса, so Russian does not need to repeat она. English usually does: The fox ran away when she saw..., but Russian naturally says just:

Лиса быстро убежала, когда увидела...

The meaning is still understood as when the fox saw...

Because белку is the direct object of увидела.

The verb увидела takes the accusative case, and белка is a feminine noun ending in -а, so in the accusative singular it changes to -у:

• белка = nominative
• белку = accusative

So:

• Лиса = the subject
• увидела белку = saw a squirrel

Because they have different jobs in the sentence.

• лиса is the subject, so it stays in the nominative case
• белку is the object, so it goes into the accusative case

Russian uses case endings to show what each noun is doing. English mostly uses word order for that, but Russian uses both word order and endings.

Because this phrase describes location, not movement.

• на дереве = on/in the tree as a place
• на дерево = onto the tree as movement toward it

Here, the squirrel is already there, so Russian uses на + prepositional case:

• дерево → на дереве

So увидела белку на дереве means she saw the squirrel located in/on the tree.

Because prepositions do not match perfectly between languages.

Russian usually says на дереве for something up in a tree, on its branches, even when English would normally say in the tree.

So this is a good phrase to learn as a set:

• белка на дереве
• птица на дереве

It sounds natural in Russian even if the English translation uses in.

Because убежала means ran away as a completed action.

This is the verb убежать, which is perfective. It focuses on the whole result: the fox got away / ran off.

By contrast:

• бежала = was running / ran
• убежала = ran away

So убежала is the better choice here because the sentence describes a completed event.

Because увидела usually expresses a single completed act of seeing/noticing.

Compare:

• видела = saw / was seeing / used to see, depending on context
• увидела = caught sight of, saw, noticed

In this sentence, the meaning is that the fox noticed the squirrel at that moment, so увидела fits better.

Because когда introduces a subordinate clause.

Russian punctuation requires a comma before clauses like:

• когда = when
• если = if
• потому что = because
• что = that

So the sentence is divided into:

• Лиса быстро убежала
• когда увидела белку на дереве

That is why the comma is necessary.

Not completely. Russian word order is more flexible than English because case endings already show who did what.

The given order is neutral and natural:

Лиса быстро убежала, когда увидела белку на дереве.

But other orders are also possible, with different emphasis. For example:

Когда лиса увидела белку на дереве, она быстро убежала.

That version puts the when-clause first and may sound slightly more narrative.

That is a very natural position for an adverb in Russian.

быстро modifies the verb убежала, and placing it before the verb is common:

• быстро убежала = quickly ran away

You can sometimes move adverbs around, but the original version sounds neutral and smooth.

Russian has no articles, so it does not have separate words for a, an, or the.

That means:

• лиса can mean a fox or the fox
• белку can mean a squirrel or the squirrel
• на дереве can mean on a tree, on the tree, in a tree, or in the tree

Context tells you which meaning is intended.

A helpful stressed version is:

Лиса́ бы́стро убежа́ла, когда́ уви́дела бе́лку на де́реве.

A few notes:

• лиса́ — stress on the last syllable
• бы́стро — stress on the first syllable
• убежа́ла — stress on жа
• уви́дела — stress on ви
• бе́лку — stress on the first syllable
• де́реве — stress on the first syllable

Learning stress early is useful because Russian stress is not always predictable.