Ja sam juče našla ključ u torbi.

Sam is the 1st person singular present form of biti (to be), and Serbian uses it to form the past tense.

So the past tense here is built like this:

• sam = auxiliary am
• našla = past active participle of naći (to find)

Together:

• ja sam našla = I found

This is a very common Serbian past-tense pattern:

• ja sam rekla = I said
• ja sam videla = I saw
• ja sam kupila = I bought

Because našla shows that the speaker is female.

In Serbian past tense, the participle agrees with the subject’s gender and number:

• našao = masculine singular
• našla = feminine singular
• našlo = neuter singular
• našli / našle = plural

So:

• a woman says: Ja sam juče našla ključ u torbi.
• a man says: Ja sam juče našao ključ u torbi.

This is one of the big differences from English: Serbian past tense often tells you the speaker’s gender.

Yes, very often.

Serbian usually does not need the subject pronoun if it is already clear from the verb form and context. So you can say:

• Juče sam našla ključ u torbi.

This still means I found the key in the bag yesterday, and it sounds very natural.

You would keep ja if you want emphasis, for example:

• Ja sam našla ključ, ne ti. = I found the key, not you.

So in many everyday sentences, ja is optional.

Because sam is a clitic, and clitics in Serbian usually go in the second position of the sentence or clause.

In:

• Ja sam juče našla ključ u torbi.

the first element is Ja, so sam comes right after it.

This is a very important Serbian word-order rule. For example:

• Juče sam našla ključ u torbi.
• Ključ sam juče našla u torbi.

In both cases, sam still tries to stay in second position.

English learners often want to place it differently, but Serbian clitics are quite strict about this.

The dictionary form is naći, which means to find.

So:

• naći = to find
• našla = found (feminine singular past form)

This verb is perfective, which means it usually refers to a completed action. That fits well with yesterday, because the action is understood as finished.

Its imperfective partner is often:

• nalaziti = to be finding / to find repeatedly / to find in an ongoing or habitual sense

Very roughly:

• našla sam = I found (completed event)
• nalazila sam = I was finding / I used to find / I kept finding

It is in the accusative, but for many masculine inanimate nouns, the accusative singular looks exactly like the nominative singular.

So:

• nominative: ključ = key
• accusative: ključ = key

That is why you do not see a change.

Compare that with a masculine animate noun, where accusative usually does change:

• vidim čoveka = I see the man

But with an inanimate noun like ključ, nominative and accusative are the same:

• imam ključ = I have a key / the key
• našla sam ključ = I found the key

Because u can take different cases depending on the meaning.

Here, u torbi means in the bag, describing a location, so Serbian uses the locative:

• u torbi = in the bag

If you were talking about movement into the bag, Serbian would use the accusative:

• stavila sam ključ u torbu = I put the key into the bag

So the contrast is:

• u torbi = in the bag, inside the bag, located there
• u torbu = into the bag, movement toward the inside

In this sentence, the key was found inside the bag, so u torbi is correct.

Torbi is the locative singular of torba.

Forms:

• torba = bag (dictionary form, nominative singular)
• u torbi = in the bag (locative singular)

So:

• torba → torbi

This is a very common pattern for many feminine nouns ending in -a:

• škola → u školi
• soba → u sobi
• torba → u torbi

Juče means yesterday, and it is quite flexible in Serbian.

Your sentence has:

• Ja sam juče našla ključ u torbi.

That is natural, but you can also say:

• Juče sam našla ključ u torbi.
• Ključ sam juče našla u torbi.

The exact word order can shift depending on emphasis and style.

A very common neutral order is:

• Juče sam našla ključ u torbi.

Putting juče first often makes the time frame slightly more prominent.

Yes, Serbian word order is more flexible than English word order, although not completely free.

These are all possible, with small differences in emphasis:

• Ja sam juče našla ključ u torbi.
• Juče sam našla ključ u torbi.
• Ključ sam juče našla u torbi.
• U torbi sam juče našla ključ.

The basic meaning stays the same, but the focus changes:

• Juče... emphasizes when
• Ključ... emphasizes what
• U torbi... emphasizes where

What usually stays important is correct placement of clitics like sam.

Torba is a general word for bag, and depending on context it can mean things like:

• bag
• handbag
• purse
• satchel
• school bag

So u torbi could mean in the bag or, in some contexts, in the purse/handbag.

The exact English word depends on the situation.

Yes, only the participle would change for gender:

• female speaker: Ja sam juče našla ključ u torbi.
• male speaker: Ja sam juče našao ključ u torbi.

Everything else stays the same.

Serbian has no articles like a or the, so ključ by itself can mean either:

• a key
• the key

The exact meaning depends on context.

So:

• našla sam ključ could mean I found a key
• or I found the key

If the meaning shown to the learner is the key, that comes from context, not from a separate Serbian word like English the.

Because the sentence refers to a single completed event in the past:

• it happened yesterday
• the key was successfully found

That is exactly the kind of situation where Serbian commonly uses a perfective verb.

So:

• našla sam sounds natural for I found

If you wanted an ongoing or repeated meaning, Serbian would more likely use an imperfective form instead, depending on the context.

So this sentence is a good example of:

• completed action
• specific past event
• perfective verb usage