Shvatila sam red vožnje.

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

In Shvatila sam red vožnje, the first element is shvatila, so sam comes right after it.

Some common patterns are:

• Shvatila sam red vožnje.
• Ja sam shvatila red vožnje.
• Red vožnje sam shvatila. — more emphasis on red vožnje

So sam shvatila at the very beginning would not be the normal word order.

Shvatila is the past participle form of the verb shvatiti.

Here it tells us:

• the action is in the past
• the speaker is female
• the number is singular

So the matching forms are:

• shvatio sam — I understood / I realized (male speaker)
• shvatila sam — I understood / I realized (female speaker)

The dictionary form is shvatiti, which is a perfective verb.

Sam is the 1st person singular present tense of biti (to be), but in sentences like this it functions as part of the past tense.

Serbian often forms the past tense with:

• a past participle +
• a short form of biti

So:

• shvatila sam = literally something like understood am, but naturally it means I understood / I realized

Other forms are:

• si — you are / you did
• je — he/she/it is / did
• smo — we are / did
• ste — you plural/formal are / did
• su — they are / did

Because Serbian usually drops subject pronouns when they are not needed.

The form sam already shows that the subject is I, and shvatila shows the speaker is female, so ja is unnecessary.

You can still say:

• Ja sam shvatila red vožnje.

But this usually adds emphasis, such as:

• I understood the timetable
• I was the one who understood it

So the version without ja is more neutral and natural in many contexts.

Because vožnje is in the genitive singular.

The expression red vožnje is a fixed and very common Serbian phrase meaning timetable / schedule. Literally, it is something like order of driving/rides/departures.

Here:

• red = order, sequence
• vožnja = drive, ride, trip
• vožnje = genitive singular of vožnja

So red vožnje works as one unit meaning schedule/timetable.

As a whole, red vožnje is the direct object of the verb, so it is in the accusative.

However, red is an inanimate masculine noun, and for many such nouns the accusative singular looks the same as the nominative singular.

So:

• nominative: red
• accusative: red

Inside that phrase, vožnje stays in the genitive singular because it depends on red.

So the structure is:

• shvatila sam — verb phrase
• red vožnje — direct object in accusative, with an internal genitive noun

Yes, shvatiti is perfective.

That means it presents the action as completed: the speaker reached understanding.

So Shvatila sam red vožnje suggests:

• there was a moment of understanding
• now the speaker has successfully figured it out

The imperfective partner is usually shvatati.

Compare:

• Shvatila sam... — I understood / I figured out
• Shvatala sam... — I was understanding / I used to understand / I was gradually getting it

In this sentence, the perfective verb sounds natural because understanding the timetable is treated as a completed result.

Yes, you could, but shvatila and razumela are not always identical in feeling.

Very roughly:

• razumeti often means to understand
• shvatiti often means to grasp, realize, figure out, catch on

In many everyday situations they overlap, and both may work. But shvatila sam can sound a bit more like:

• I got it
• I figured it out
• it clicked

So in this sentence, shvatila sam is very natural if the idea is that the speaker finally understood how the timetable works.

Yes. Serbian word order is fairly flexible, but changing it usually changes the emphasis.

For example:

• Shvatila sam red vožnje. — neutral
• Ja sam shvatila red vožnje. — emphasis on I
• Red vožnje sam shvatila. — emphasis on the timetable
• Shvatila sam red vožnje, ali ne i cenovnik. — emphasis shaped by contrast

Even though the order can change, the clitic sam still tends to stay in second position.

Yes, that is a very good idea.

Even though it is built from separate words, red vožnje is such a common expression that it is best learned almost like a single unit, just like English speakers learn bus schedule or train timetable as set phrases.

You will also see related expressions such as:

• autobuski red vožnje — bus timetable
• red letenja — flight schedule
• po redu vožnje — according to the timetable

Learning red vožnje as a chunk will make it easier to recognize and use naturally.