How do we emphasize the urgency of a situation or immediacy of an event? How can we reassure someone that something will be taken care of right away?

The adverb gleich is used a lot and has many possible translations in this context. You might be thinking about it as an adjective meaning "same" or "alike," and we also have a lesson on that topic. But here we are looking at how it is used to define something as happening "in just a minute," "immediately," or "momentarily." 

Gut, vielen Dank. Ich mache mich gleich auf den Weg.

Good, many thanks. I'll be on my way immediately.

Caption 14, Berufsleben - Probleme mit Mitarbeitern

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Warum hab ich das nicht gleich erkannt?

Why didn't I realize that right away?

Caption 80, Die Pfefferkörner - Endspurt - Part 12

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Ja, Moment, ich habe es gleich.

Yes, one moment, I'll have it momentarily.

Caption 30, Der Merkelpilot - der kleine Mann, der es macht

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There is another way to say that something will happen "any minute now," and it's very similar to how it's said in English:

Aber der Reparaturdienst müsste jede Minute da sein.

But the repair service should be here any minute.

Caption 8, Die Pfefferkörner - Endspurt - Part 18

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Another adverb to know is sofort, which is even more urgent than gleich, and is pretty much always translated as "at once," "right away," or "immediately."

Kein Problem, Frau Schmidt. Ich werde es Ihnen sofort schicken.

No problem, Ms. Schmidt. I will send it to you immediately.

Caption 67, Berufsleben - das Vorstellungsgespräch

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Sie ist sofort abgehauen, als Frau Lenz die Sache angesprochen hat.

She immediately took off when Ms. Lenz raised the matter.

Caption 65, Die Pfefferkörner - Endspurt - Part 2

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In more formal contexts, you may hear unverzüglich ("without delay") and umgehend. 

Er muss unverzüglich Waffenstillstandsverhandlungen mit Eisenhower und Montgomery aufnehmen.

He must immediately begin armistice negotiations with Eisenhower and Montgomery.

Caption 81, Die Stunde der Offiziere - Dokudrama über den 20. Juli 1944

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Oder noch besser, komm umgehend ins Kontor.

Or better yet, come to the office immediately.

Caption 65, Die Pfefferkörner - Alles auf Anfang

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Although unmittelbar is also translated as "immediate," it is often related to space rather than time: 

Wir sind, äh, hab ich schon gesagt,

We are, uh — as I've already said —

in unmittelbarer Nähe, äh, von Saarbrücken.

in the immediate vicinity, uh, of Saarbrücken.

Captions 37-38, Nachbarn - Andrea aus Forbach

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Daher ordne ich an, dass Sie unmittelbar wieder die Ehe schließen.

Therefore I order you to remarry immediately.

Captions 34-35, Yabla Gerichtshof - Probleme des Zusammenlebens

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For urgency, there is the word dringend, which like many German words functions as both an adjective and an adverb depending on how it's integrated in the sentence: 
 

Ich brauche dich hier dringend im Innendienst.

I need you urgently here in the office.

Caption 63, Großstadtrevier - Von Monstern und Mördern

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Further Learning
You will find many examples of these words used on Yabla German. In particular, keep an eye on how the translation of gleich changes depending on the context. 

Neunzehnhundertdreiunddreißig: This many letters in one single word looks pretty difficult, but the year it's expressing, 1933, is more difficult yet. It's now 90 years since the Nazis came into power in Germany, and many German states and communities are organizing events in remembrance of the lives that were lost as a result. There will also be lot of stories in the German media about the first terrible actions taken by the Nazis after they came into power.

Es gibt keine guten Nachrichten mehr,

There is no good news anymore,

jedenfalls nicht mehr seit Januar 1933.

at least not since January 1933.

Captions 77-78, Die Stunde der Offiziere - Dokudrama über den 20. Juli 1944

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Adolf Hitler came into power in Germany on January 30th, 1933. This is sometimes referred to as die Machtergreifung ("seizure of power"), but this term is often perceived as incorrectly suggesting that the German populace was passively, rather than actively, participating in and approving the event. Hence, when it appears in German media, it is usually seen with quotation marks as die sogenannte „Machtergreifung“ (the so-called "seizure of power"). A better and more neutral term is die Machtübergabe ("the transfer of power").

Den Anfang macht das Reichstagsgebäude.

The parliament building started it.

Caption 11, Berlin - Hauptstadt des vereinten Deutschland

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The caption above is in an entirely different context, but one of the first actions the Nazis took, on February 1st, 1933, was to dissolve der Reichstag, or parliament. This marked the end of democracy in Germany until the founding of the Federal Republic of Germany in 1949 in the west, and the re-unification of the former German Democratic Republic in 1990 in the east. In today's context, only the building is referred to as der Reichstag. The modern name for the German parliament that meets in the Reichstag building is der Bundestag.

1933, als der Reichstag brennt,

In 1933, when the Reichstag burned,

beginnt eine Zeit, die man Drittes Reich nennt.

a period called the Third Reich began.

Captions 34-35, Rapucation - Lernen durch Rapmusik

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The decree that robbed German citizens of any protection under the constitution was put into effect on February 28th, 1933, the day after the Reichstag fire. Regardless of who set the Reichstag ablaze, the Nazis exploited the fire to issue an "emergency decree," which suspended all civil liberties for German citizens and paved the way for the Nazi dictatorship.

Die Konzentrationslager sind beschleunigt zu besetzen ...

The concentration camps are to be occupied immediately ...

Caption 52, Die Stunde der Offiziere - Dokudrama über den 20. Juli 1944

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As soon as the Nazis were in power, they began arresting and murdering their first victims, who were mostly political opponents, including members of parliament, city mayors, and other members of opposition parties such as the SPD and KPD. They were taken to so-called wilde Konzentrationslager ("spontaneous concentration camps") such as KZ Columbia-Haus, a building near Tempelhof Airport in Berlin that was later torn down. Dachau Concentration Camp was already constructed and taking in prisoners by March 22nd, 1933. Unfortunately, it was the first of many hundreds of such facilities designed to exploit prisoners by working them to death—Vernichtung durch Arbeit, "extermination through work"—or outright murdering them.

Germany has accomplished a lot in memorializing the terrible events that resulted from the Nazi Regime coming to power in 1933. A large part of the German government's hesitation in getting involved in armed conflicts probably comes from historical experience of the potential cost to human life and infrastructure. So although other wars and genocides have occurred after the Second World War, let us hope, especially in view of the current conflict in Ukraine, that rational humanitarian thinking and peace can prevail.

Further Learning
Make a list of some of the German terms above and read the linked Wikipedia articles. If you're feeling brave, you can find the German-language versions and give them a go. Then find the terms on Yabla German and see how they are used in different contexts.