All three of the words above can mean "occupied," yet there are certain situations in which only one is applicable. They also have other unrelated definitions that can cause a bit of confusion.

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The adjective besetzt means that something is in use. It is used for seats, taxis, phone lines, rooms, and toilets. It is also used to denote people occupying a place in protest.

Ein wenig Ruhe täte jetzt gut, aber dieser Platz ist schon besetzt.

A little rest now would do it good, but this place is already occupied.

Caption 21, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen

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Die Leitwarte ist rund um die Uhr besetzt.

The control room is staffed around the clock.

Caption 24, Ab in den Urlaub: So kommt der Koffer in den Flieger

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Die Klimaaktivisten, die den Ort besetzt haben, wollen nicht kampflos aufgeben.

The climate activists who have occupied the site don't want to give up without a fight.

Captions 48-49, Langsam gesprochene: Nachrichten Gewalt in der Silvesternacht

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The word belegt suggests something has been assigned, reserved, or is already taken. It can be used when talking about food. The verb etwas belegen also means "to prove" or "to document." You might know the word der Beleg (the receipt) from when you do your shopping!

Die besten Plätze sind schnell belegt.

The best places are quickly occupied.

Caption 43, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen 

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Nun muss ich meinen Teig nur noch mit den Apfelstücken belegen.

Now I just have to cover the batter with the apple pieces.

Caption 29, Apfelkuchen mit Eva

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Es gibt tatsächlich keine einzige Studie, die belegt, dass die Dämpfung uns vor Verletzungen schützt.

In fact, there is not a single study that proves that the cushioning protects us from injuries.

Captions 20-21, Gesundheit: Warum Barfußlaufen vor Verletzungen schützen könnte

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The adjective beschäftigt means busy or occupied. It usually refers to people and can mean they are working or too busy to do something. It can also mean "employed" or "preoccupied."

Dann ist auch die Mutter damit beschäftigt, Nahrung herbeizuschaffen.

Then the mother is also occupied with providing nourishment.

Caption 31, Alpenseen: Kühle Schönheiten

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Auf der Baustelle werden mehrere Tausend Menschen beschäftigt sein.

At the construction site, several thousand people will be employed.

Caption 28, Die Insel Fehmarn So wird der Fehmarnbelt-Tunnel gebaut

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Trotzdem hat mich dieses Thema immer wieder beschäftigt.

Nevertheless, this topic has always preoccupied me.

Caption 23, Deutsch mit Eylin: Weniger müssen, mehr dürfen

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Further Learning

You'll find many more examples on Yabla German. Particularly for besetzt and belegt, have a look and compare the situations they are used in. 

We all hate it, but it's simply a part of life: Waiting in line. 

In German, the verb for "to wait" is, of course, warten:

Wenn die denkt, ich warte hier noch lange, dann hat sie sich aber getäuscht.

If she thinks I'm going to wait here a long time, then she's wrong.

Caption 18, Weihnachtsmann gesucht: Bist du verliebt?

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But when we talk about waiting in line, there are a few other applicable phrases. The first one is (für etwas) anstehen, or "to stand in line (for something)."

Beim Trampolin gibt es eine ganz schön lange Schlange zum Anstehen.

At the trampoline there is quite a long line that you have to stand in.

Caption 16, Das Fest: Open-Air in Karlsruhe

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As you can see, the word for "line" or "queue" in this sense is die Schlange, which is also the word for "snake" in German. You will also hear die Warteschlange.

Und wie ihr sehen könnt, ist dort schon eine Schlange.

And as you can see, there is already a line there.

Caption 18, Eva zeigt uns: Currywurst

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The expression Schlange stehen also means "to stand in line" or "to queue."

Die stehen richtig Schlange. Was für ein Gedränge!

They are really standing in line. What a crowd!

Caption 41, Abenteuer Nordsee: Unter Riesenhaien und Tintenfischen

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If you are ever trying to get in line and are uncertain about whether someone is waiting or not, you can politely ask Stehen Sie an? or Stehen Sie in der Schlange? Hopefully, it won't be long before you hear one of these magical phrases:

Äh, der Nächste, bitte. 

Uh, next, please. 

Caption 37, Mensch Markus: Der Lottogewinner

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Und was darf's sein?

And what would you like?

Caption 48, Großstadtrevier: St. Pauli rettet HSV

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Los, jetzt bist du dran.

Go ahead, now it's your turn.

Caption 45, Die Pfefferkörner: Alles auf Anfang

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Was hättest du denn gern?

So what would you like?

Caption 5, Nicos Weg: Ich bin neu hier

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You may also hear Bekommen Sie schon?, which is a bit like "Have you already been helped/served?" or just a simple Bitteschön! 

Further Learning
Visualize yourself trying to get in line at a bank, bakery, or doctor's office. How would you ask where the line begins, who is waiting, and who is already being helped? You can also go on German Yabla and see the ways the phrases are being used by native German speakers.

The noun der Beleg, the verb belegen and the adjective belegt have related roots, but are used differently in a variety of contexts. Let's start with the noun der Beleg.

Du brauchst einen Ort, an dem deine Belege sicher sind.

You need a place where your documents are safe.

Caption 7, Reposito - in 60 Sekunden

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BANNER PLACEHOLDER

Der Beleg is often translated as "evidence," "proof," "document," "documentation," "voucher," or "receipt." In everyday life in Germany, I probably hear it most often when leaving the cash register at the supermarket after having paid: Möchten Sie den Beleg haben?

Now onto the verb belegen: 

Nun muss ich meinen Teig nur noch mit den Apfelstücken belegen.

Now I just have to cover the batter with the apple pieces.

Caption 29, Apfelkuchen - mit Eva

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Unfallstudien belegen sogar, dass Autos mit hoher passiver Fußgängersicherheit

Accident studies even prove that cars with a higher passive [automatic] protection for pedestrians

für den Unfallschutz von Radfahrern kaum helfen.

barely help in the protection of cyclists from accidents.

Captions 12-13, Crashtest - Fahrradfahrer profitieren kaum vom Fußgängerschutz am Auto

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Wie man hier sieht, haben wir auch frisches Gemüse

As you see here, we also have fresh vegetables

wie Tomaten, Gurken,

like tomatoes and cucumbers

da wir frisch, äh, Sandwiches und Brötchen belegen.

since we make fresh sandwiches and rolls.

Captions 21-23, Berlin - Judith und die „Brezel Bar“

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In most cases, belegen is usually translated as to "to cover," "to prove," or "to document." In the last example, however, an open-faced sandwich is a belegtes Brot in German. Thus when you literally "cover" sandwiches and bread rolls, you are in fact "making" them. Again, understanding properly all depends upon the context!

The verb belegen can also be translated as "to occupy" or "to take," at least in the sense that you "occupy" a position in a race or "take" a university course: 

Nürnberg belegt jetzt Platz fünfzehn...

Nuremberg is now in fifteenth place...

Caption 46, FC Bayern München - in einer eigenen Liga

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Na ja, in der Justizvollzugsanstalt Fuhlsbüttel kannst du ja einen Kursus belegen als Alleinunterhalter.

Well, at Fuhlsbüttel Penitentiary you can take a class to become a solo entertainer.

Caption 66, Großstadtrevier - St. Pauli rettet HSV

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Last but not least, let's take a look at belegt as an adjective: 

Die besten Plätze sind schnell belegt.

The best places are quickly occupied.

Caption 43, Abenteuer Nordsee - Unter Riesenhaien und Tintenfischen

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Drei Damen vom Grill, die eine belegte Schrippe mit 'ner Bulette gefüllt haben [Inhaber]

Three ladies from the grill who have filled an open-faced roll with a meatball [owner]

und das Hamburger genannt haben.

and called that a hamburger.

Captions 14-15, Berlin - Die beste Auswahl an Hamburgern

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Further Learning
See if you can find other examples of der Beleg, belegen, and belegt on Yabla German and find a tandem partner to take turns making up and checking your own sentences using these words.