You know the German word frei, but this is rarely used to describe the price of items or services. However, there are many words for this.

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You can talk about something being kostenfrei, which is essentially synonymous with kostenlos. 

Der Eintritt ist für die Kinder kostenfrei.

The admission is free for children.

Caption 45, Theaterstück über gesunde Ernährung: Henrietta in Fructonia

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Ab März ist der öffentliche Nahverkehr kostenlos.

Public transport is going to be free starting in March.

Caption 30, Deutsch mit Eylin: Satzanfänge

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Ich möchte mich noch einmal sehr bedanken, dass die Anzeige kostenlos abgedruckt wird.

I would like to thank you very much once again for publishing the ad free of charge.

Captions 19-20, Nicos Weg B1: In der Redaktion

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You might also see the word gratis, which comes from Latin. 

Wer sein Busticket gegen einen Diesel eintauscht, erhält einen Duftbaum gratis.

Anyone who exchanges their bus ticket for a diesel car will receive a tree-shaped air freshener for free.

Captions 9-10, extra 3: Öffentlicher Personennahverkehr (ÖPNV)

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The word umsonst has two different meanings. It can be translated as "free of charge," but also as "without reason" or "in vain." 

Dass Sie nicht denken, dass in Berlin dann alles umsonst ist.

So that you don't then think that everything is free in Berlin.

Caption 41, Jonathan Johnson: Nahöstliches Essen in Berlin

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Der Freizeitpark heißt nicht umsonst Europa-Park.

The theme park is not called Europa-Park without reason.

Caption 19, Deutsche Welle: Hin und weg Best of Europa-Park!

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Another word that means "without money," "unpaid," or "free of charge" is unentgeltlich, which is generally used in writing or more formal contexts. 

Further Learning
You can find all of these words on Yabla German. Also, check out our lesson on various words for "cheap" or "inexpensive" in German.