When I say "foreign language" I mean a language that you know nothing about. I'm not talking about singing in French when you studied French in high school and know how to say "Would you like to walk with me tonight?" I'm talking about singing in a language like Euskara.
It's probably just like memorizing. Different people have different methods. Some people even believe that learning a song with a foreign language is easier than learning a song with text in their native tongue.
Starting small and building up to whole phrase
Everyone knows that sentences can be phrased: "I have two cats." That is a sentence. You can emphasize different parts of the sentence to do what we call "phrase" the sentence. Emphasize "I," in the sentence and you turn all attention to "I." Emphasize "cats," and all of the sudden, no one will doubt that you are not talking about dogs. You can also emphasize "two" by taking time to say it and say it hesitantly and very soft. These are some ways to phrase a sentence. In music you can do the same thing.
Les trois souris aveugles
Think of the tune that goes to "Three Blind Mice." Now, think of the first three words and notes: "Three blind mice," start on the E right above middle C. The notes are: E, D, C, right?
Of course, "Three blind mice" is hardly a sentence, and the motif of E,D,C is not terribly interesting, but if you apply the same exercise to these three words and notes as we did in the previous "I have two cats." exercise, you will see that you can create some pretty amazing dynamics by changing the emphasis or building intensity to "mice" or emphasizing "Three" and making "blind mice" softer. The possibilities are endless.
Note by note, phrase by phrase, know what you are singing
So now to the foreign phrases. Every phrase of music is structured carefully by the composer. If the composer has set some text to the music, he (or she) either knows the language or has studied it enough to know what makes sense in terms of phrasing and rhythm. As singers, we need to trust the composer and follow the guidelines written in the music. This is where, learning phrase by phrase comes in.
Just as if you were learning a dance step, you need to be able to move from one note to the next with ease. After you can sing two notes with the syllables attached, try adding the next note and syllable. Try singing the second and the third, then the second then the third. Put the three together. Add the fourth note and syllable now. Sing the third and the fourth in a repeated pattern. Sing the second, third and fourth. Practice slowly and accurately, while slowly speeding the tempo until you get it to a comfortable speed.
Don't forget that you are telling a story.
Do you know what you are singing? Literally? You should know what you are saying literally and what the phrase means in your language. You will be able to tell the story as if it is your own to tell. You should also study the other parts, especially when you are singing choral music since sometimes the text dove-tails between the voice parts. But, this also applies when you are singing art songs and arias. Many times the orchestral part or piano part will have different colors and textures that enhance the story you are telling with your song. You, as a singer, will be captivating if you play on all the magic available to you.
Extaordinary does not come easily.
Some people think singing is easy. I think singing well is one of the most difficult disciplines. Not only are you the instrument that makes the beautiful sound; that requires many, many hours of practice and dedication to craft, but you have to be able to sing in tune. You also need to sing so that no matter what you sing, if a person in the audience understands the language you are singing, they should be able to understand every word and overall meaning or picture you are portraying. Even if the person in the audience does not understand the language you are singing, they still should hear the story that you are telling.
With a musical instrument, all you need to do is tell a story with the phrasing and accurate notes, dynamics and rhythm. There are no words. Words put a whole new dimension into the mix. Especially when you are singing in a language that is not familiar to you, you need to be all the more diligent in practicing the art.