Saqué un notable en el dictado y un sobresaliente en la redacción, así que salí de clase bastante contenta.

Yes, sacar often does mean to take out, but it has several common meanings.

In school contexts, sacar is very often used to mean to get, to score, or to obtain a grade:

• Sacar un notable = to get a notable
• Sacar un 8 = to get an 8
• Sacar buena nota = to get a good grade

So in this sentence, saqué means I got / I scored.

It is the 1st person singular preterite of sacar:

• yo saqué = I got / I scored

They are names of grades in the Spanish grading system, especially in Spain.

Very roughly:

• aprobado = pass
• notable = a very good grade
• sobresaliente = an excellent grade

A common rough equivalence is:

• notable ≈ around 7–8.9 / 10
• sobresaliente ≈ around 9–10 / 10

So the speaker is saying they did well in both tasks, and even better in the second one.

In this context, the grade labels are being used as nouns:

• un notable
• un sobresaliente

That is why they take the article un.

It is similar to saying:

• I got a pass
• I got an excellent

Even though notable and sobresaliente are also adjectives in other contexts, here they function as grade nouns.

Here en means something like in or on, depending on how English would express it.

It is used to show the activity, test, or piece of work where the grade was obtained:

• en el examen = in/on the exam
• en el dictado = in/on the dictation
• en la redacción = in/on the composition

So:

• Saqué un notable en el dictado = I got a notable in/on the dictation

English may prefer in or on depending on the situation, but Spanish commonly uses en here.

In school Spanish:

• dictado = dictation
  The teacher reads a text aloud, and students write it down. This is often used to practise spelling and listening.

• redacción = composition, essay, or piece of writing
  It usually refers to a written exercise where the student has to write a text.

So these are two different school tasks:

• one based on listening and writing what is heard
• one based on writing your own text

They are in the preterite because the sentence describes completed actions in the past:

• Saqué un notable... = I got a notable...
• salí de clase... = I left class...

The speaker is talking about a specific occasion: they got those grades, and then they left class feeling happy.

The forms are:

• saqué = preterite of sacar
• salí = preterite of salir

If the sentence were describing a habitual situation, Spanish would probably use the imperfect instead.

Así que means so, so that’s why, or as a result.

It connects the first part of the sentence with the consequence:

• I got good grades, so I left class quite happy.

It shows a result or conclusion:

• good grades → happy feeling

It is very common in everyday Spanish.

Compare:

• porque = because → gives a reason
• así que = so → gives a result

Here the structure is:

• cause: good grades
• result: left class happy

Salir de clase is a very common expression meaning to leave class or to come out of class.

In Spanish, some expressions with places or activities often appear without the article when speaking in a general, idiomatic way:

• estar en clase = to be in class
• salir de clase = to leave class
• ir a clase = to go to class

If you say de la clase, it sounds more specific:

• leaving that particular classroom
• leaving that specific class

So:

• salí de clase = the normal idiomatic expression
• salí de la clase = more literal/specific

Because the speaker is female.

Contento/contenta is an adjective, so it agrees with the person it describes:

• contento = masculine
• contenta = feminine

Since the sentence says:

• salí de clase bastante contenta

the speaker is telling us she is a woman or girl.

If the speaker were male, it would be:

• salí de clase bastante contento

This is one of the things Spanish can show that English usually does not.

Here bastante means quite, fairly, or pretty.

So:

• bastante contenta = quite happy / pretty happy

It softens the adjective a little compared with muy:

• muy contenta = very happy
• bastante contenta = quite happy

Also, in this use, bastante does not change form:

• bastante contenta
• bastante contento
• bastante felices

Because Spanish often leaves out subject pronouns when they are clear from the verb form.

Here:

• saqué already means I got
• salí already means I left

So yo is unnecessary unless the speaker wants emphasis or contrast:

• Saqué un notable... = normal
• Yo saqué un notable... = more emphatic, like I got a notable...

This omission of subject pronouns is very common in Spanish.