If I receive a call for my friend and he/she is sitting beside me, what should I say in German? In English, I'd say:
Just hold on while I give him/her the receiver.
Just hold on, I'll give him/her the receiver.
jp-jee proposed the phrase:
Moment, ich gebe dich/Sie weiter.
Here, the calling person is "given" to the called person. Another variant is to interchange who is given to whom:
Moment, ich geb' sie/ihn dir/Ihnen.
Here, the called person (accusative, sie=fem./ihn=male) is "given" to the calling person (dative, dir=familiar/Ihnen=polite). In my opinion this variant is more common than the first one.
If the person is sitting beside you, you can say:
Warten Sie kurz, ich gebe ihm/ihr den Hörer. (formal, literal translation)
Warte kurz, ich geb' ihm/ihr den Hörer. (informal, literal)
Ich gebe ihn/sie Ihnen (gleich). (another formal variant)
Ich geb' ihn dir (gleich). (informal)
In my opinion, "ich gebe Dich/Sie weiter" would also be used in some bigger institution's telephone network, like "ich stelle Sie durch", "ich leite Sie weiter" and "ich verbinde Sie gleich mit ihm/ihr".
The word you're looking for is "der (Telefon)hörer". The literal translation is "the listener", but in context of telephones it was the word for the "bone".
Ich lege den Hörer auf.
I put down the receiver.
Ich nehme den Hörer ab.
I pick up the receiver/the phone.
The most literal translation of your sentence would be:
Ich gebe ihr/ihm den Hörer.
And people do say that even with wireless phones that have a base station somewhere. For a cell phone. There, you would just pass on the "Handy". The suggestions of the other answers are fine as well.
Prove for the phrase being used millions of times in various registers: