What is a "first chair" or "principal" musician called?
I have searched in Google translate and got "erster Stuhl Trompeter", but that sounds a little too literal.
The wind instruments are numbered individually so here you can indeed say “erste Trompete”, but the strings aren't, so in particular, “erste Geige” does not mean principal but the whole group of violinists who play the first voice (of which there can be 6-14 in an orchestra!).
The general term for first chair is “Stimmführer”. (Yes, that's the same word root as Hitler liked to be called, so never shorten it to “Führer” alone! The root also appears in a number of other composites, like “Führerschein” – driver's licence, which don't have a nazi connotation.) For the principal of the first violins specifically, there is also the word “Konzertmeister”.
To clear this up:
In orchestras, not people but instrumental parts are numbered. Therefore there is the "erste Trompete", which might as well consist of more than one trumpet.
Same applies for violins, where there are "erste Geige(n)" and "zweite Geige(n)" (note that these can be refered to in singular or plural). For each instrumental part, the person sitting closest to the audience is the "Stimmführer", sitting on the "erstes Pult".
A special role is assigned to the "Stimmführer" of the "erste Geige", who is something like the leader of the orchestra, therefore the "Konzertmeister".
As mentioned in other answers, usually instrumental parts are numbered. "Erste Trompete, zweite Trompete, erste Klarinette, erste Geige, zweite Geige, ...".
A special role is given to the leader of the first violin - he is called "Konzertmeister" (concert master) or "1. Pult".
If one person from the section is assigned the leading role for the entire section, it is mostly the (or one of the) first part and he is called the "Stimmführer". He's then responsible for the entire section (for example all Clarinets or all Trumpets).