Die Schülerin malt das Bild mit einem blauen Buntstift aus.

Die Schülerin is the subject of the sentence — the person doing the action.

• die = the definite article for a feminine singular noun in the nominative
• Schülerin = female pupil / schoolgirl / female student

So Die Schülerin means the female student is the one who is coloring or painting.

This also tells you that Schülerin is feminine. The masculine form would be der Schüler.

German nouns have grammatical gender, and the article changes to match the noun.

Here:

• die Schülerin → feminine
• das Bild → neuter

So the articles are not chosen by meaning alone, but by the grammatical gender of each noun:

• die for Schülerin
• das for Bild

You just have to learn the noun together with its article:

• die Schülerin
• das Bild
• der Buntstift

Das Bild is the direct object — it is the thing being colored.

The verb here is ausmalen, and what is being ausgemalt?
das Bild

That makes das Bild accusative. But for a neuter singular noun with the definite article, the nominative and accusative forms are the same:

• nominative: das Bild
• accusative: das Bild

So even though it is accusative here, the form does not change.

Because the preposition mit always takes the dative case.

The noun phrase is:

• mit = with
• einem = dative singular masculine form of ein
• blauen = adjective ending used here in the dative masculine phrase
• Buntstift = colored pencil / coloring pencil

Why masculine? Because Buntstift is der Buntstift.

So:

• nominative: ein blauer Buntstift
• dative after mit: mit einem blauen Buntstift

Because adjective endings in German depend on:

1. the case
2. the gender
3. the article before the adjective

Here the phrase is mit einem blauen Buntstift:

• mit requires dative
• Buntstift is masculine
• einem already shows case and gender

After einem in the dative masculine, the adjective usually takes -en:

• mit einem blauen Buntstift

So blauen is correct because it matches a masculine singular dative noun phrase with an ein-word article.

Because ausmalen is a separable verb.

Its parts are:

• aus- = separable prefix
• malen = base verb

In a normal main clause, the conjugated verb goes in the second position, and the separable prefix goes to the end:

• Die Schülerin malt das Bild mit einem blauen Buntstift aus.

So:

• malt = conjugated verb part
• aus = prefix moved to the end

This is very common in German:

• anrufen → Ich rufe dich an.
• aufstehen → Er steht früh auf.
• ausmalen → Sie malt das Bild aus.

This is a very common learner question.

• malen usually means to paint or to draw
• ausmalen usually means to color in, to fill in with color, or sometimes to paint completely

So:

• ein Bild malen = to paint/draw a picture
• ein Bild ausmalen = to color in a picture

In this sentence, ausmalen strongly suggests that the student is coloring in the picture, not creating it from scratch.

Not in a normal main clause.

In a main clause, a separable verb splits:

• Die Schülerin malt das Bild aus.

But in some other structures, it stays together, for example:

• Sie will das Bild ausmalen.
• Weil die Schülerin das Bild ausmalt, ist sie beschäftigt.

So:

• main clause → malt ... aus
• infinitive / subordinate clause → ausmalen / ausmalt

Der Buntstift means colored pencil or coloring pencil.

It is made from:

• bunt = colorful / multi-colored
• Stift = pen, pencil, stick-like writing instrument

In everyday English, colored pencil is usually the best translation.

So mit einem blauen Buntstift means the student is using a blue colored pencil.

The exact order is not completely fixed, but there are important rules.

The main rule is:

• in a main clause, the conjugated verb must be in second position
• with a separable verb, the prefix goes to the end

So this sentence is correct:

• Die Schülerin malt das Bild mit einem blauen Buntstift aus.

But you could also change the emphasis:

• Mit einem blauen Buntstift malt die Schülerin das Bild aus.
• Das Bild malt die Schülerin mit einem blauen Buntstift aus.

These are grammatical, but they change what is emphasized.

What you cannot change is:

• malt must stay in second position in a main clause
• aus must stay at the end

Because German article use works differently from English.

In English, you might say:

• with a blue colored pencil

German expresses that with one article plus adjective endings:

• mit einem blauen Buntstift

The article einem and the adjective ending -en together give the grammatical information. German does not need another extra word.

Not exactly.

Schülerin usually means a female school student / pupil, not a university student.

Compare:

• die Schülerin = female school pupil/student
• die Studentin = female university student

So if the context is school, Schülerin is exactly right.

Yes. Native speakers often shorten it depending on context.

For example:

• Die Schülerin malt das Bild aus.
• Sie malt das Bild mit einem blauen Buntstift aus.
• Die Schülerin malt mit einem blauen Buntstift aus.
  This one only works if das Bild is already understood from context.

The full sentence is useful for learning because it clearly shows:

• the subject
• the direct object
• a mit phrase in the dative
• a separable verb

Malt is:

• 3rd person singular
• present tense
• from the verb malen

The subject is die Schülerin, which is she, so German uses the 3rd person singular form:

• ich male
• du malst
• er/sie/es malt

Since the full verb is ausmalen, the main-clause form becomes:

• sie malt ... aus

So malt agrees with die Schülerin.