The two most common meanings of the verb ausmachen are "to turn something off" and "to bring something to a conclusion with someone, to arrange something, or to agree on something." These are the first two definitions listed in the academic Digitales Wörterbuch der deutschen Sprache (DWDS) from the Berlin-Brandenburg Academy of Sciences and Humanities. Interestingly, both of these usages are listed as slang.

The commercial dictionary publisher Duden lists the two definitions as numbers one and three, respectively, but only lists the "turning off" definition as slang.

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It does make you wonder: Should the most widely used version of a word still be considered slang?

TURN IT OFF!

Jetzt mach doch bitte mal den Fernseher aus!

Now please turn off the television!

Caption 12, Lerchenberg: Du bist, was du isst

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Ey DJ! DJ, mach die Musik aus!

Hey DJ! DJ, turn the music off!

Caption 70, Laserkraft 3D: Nein, Mann

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Was bedeutet es, wenn wir das Licht ausmachen?

What does it mean when we turn out the light?

Caption 56, Kinder lernen: Wie aus Wind Strom gemacht wird

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Aber ein Hund, ne? -Machen Sie die Kamera jetzt aus.

But a dog, right? -Turn the camera off now.

Caption 30, Kurzfilm-Festival: Nicht nur der Himmel ist blau

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A less informal way to ask somebody to turn a device off would be to use the verb ausschalten.

MAKE ARRANGEMENTS

Die Mitarbeiter stellen uns den Kontakt zu den jeweiligen Ansprechpartnern her, so dass wir alle nötigen Infos vorab schon einmal erfragen und die Drehtermine ausmachen können.

The staff puts us in touch with the respective contact person so that we can request all the necessary information in advance and set up the dates for the shoot.

Captions 10-12, Rund um den Airport: Hinter den Kulissen

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Und da haben wir auch, direkt auch, einen Songwriting-Termin ausgemacht.

And then we also arranged a songwriting session right away.

Caption 31, LOTTE & Max Giesinger: Interview

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Ihr könnt doch hier nicht einfach alles ausräumen. So war das nicht ausgemacht.

You can't just clear out everything. This is not what was agreed upon.

Captions 14-15, Lilly unter den Linden: Umzug in die DDR

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A more formal way to agree to something or arrange something would be to use the verb vereinbaren.

Yet a third meaning of ausmachen combines the verb with a dative pronoun (mir, dir, euch, Ihnen, uns). It's often translated as "would you mind," or "if it doesn't disturb you" etc.

Würde es dir was ausmachen, wenn du allein kommst?

Would you mind coming alone?

Caption 71, Meine fremde Freundin: Was alle denken

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Further Learning
Go to the DWDS and Duden definitions linked above and learn a couple of the less-used meanings of ausmachen. Then go to find some more examples on Yabla German to see ausmachen used in a real-world context.

In today's lesson, we'll look at the many different meanings of the German verb ausmachen, which is a separable verb. 

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If we look at the parts of this verb, machen means "to do" or "to make" and aus means "out," "off," or "over." This will help us, but only to a certain extent. First, we have a very common translation of ausmachen, which is "to turn off":

Handys bitte ausmachen!

Please turn off your cell phones!

Caption 31, Verstehen Sie Spaß?: Sascha Grammel

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So, Annakind, jetzt wird aber Licht ausgemacht.

So, little Anna, now the light will be turned off.

Caption 17, Filmtrailer: Als Hitler das rosa Kaninchen stahl

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Next, it can also mean "to put out" when it comes to fire, and is used instead of the verb löschen ("to extinguish"):

Mit wenigen hundert Litern können wir einen Wohnungsbrand ausmachen.

With a few hundred liters we can put out an apartment fire.

Caption 87, Feuerwehr Heidelberg: Löschfahrzeug

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Willst du nicht mal die Zigarette ausmachen?

Don't you want to put out the cigarette?

Caption 1, Lerchenberg: Viva La Television!

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The verb ausmachen can be used if you've made an agreement with someone or arranged something: 

Wir hatten doch ausgemacht, dass wir uns duzen!

But we had agreed that we'd address one another informally!

Caption 3, Konjugation: Das Verb „können“

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Und da haben wir auch, direkt auch einen Songwriting-Termin ausgemacht.

And then we also arranged a songwriting session right away.

Caption 31, LOTTE & Max Giesinger: Interview

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You can use ausmachen to state that something matters or has an effect:  

...wie unheimlich viel das ausmacht, wenn jemand einfach so 'nen Laden gut im Griff hat.

...how incredibly much it matters when someone simply has a good grip on the shop.

Captions 24-25, Live-Entertainment-Award: Glamouröse Preisverleihung

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And in a related usage, it's very common to use the following construction to inquire about a potential negative effect, bother, or inconvenience:

Würde es Ihnen denn was ausmachen, wenn wir ...

Would it be a problem for you then if we...

Caption 40, Weihnachtsfilm: Ein Sack voll Geld

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Yet another translation is "to form," "to constitute," or "to comprise":

Du hast einen Zauber, der dich ausmacht.

You have a magic that forms you.

Caption 14, Cris Cosmo: Herzschlag

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Wien besitzt viele unterschiedliche Parkanlagen und ist weltweit eine der Städte mit dem höchsten Grünflächenanteil, der die Hälfte des Stadtgebiets ausmacht.

Vienna has many different parks and is one of the cities worldwide with the largest percentage of green areas, which comprise half of the city's space.

Captions 19-21, Reisebericht: Wien

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Be careful, as "to make out" in English has meanings that ausmachen does not. We might say, "I could make out the shape of her house in the distance" or "I couldn't make out what he wrote" in English, but other German verbs (such as erkennen or entziffern) are generally used in these contexts. The common slang usage of "to make out" in English that involves kissing has its own verb in German, which is knutschen, and ausmachen also isn't used for the idea of "making out well" in a deal or situation.

Further Learning
Create a sentence using each definition of ausmachen and etwas ausmachen listed above. You will find many more examples on Yabla German if you do a quick search.