If so, is there a way to "learn" how to dream in another language? For example would thinking in 'language X' for one hour before going to bed help? Or does dreaming in another language only occur when one fully starts to think in this language?
Dreaming may help but it signals that you are quite proficient in your speaking abilities.
Dreaming in another language can help by allowing you to "speak" with that language. But this may fool you as you might not be actually be speaking the way you think you are:
One interesting aspect of dreams in bilinguals is that some people have reported speaking a language fluently in a dream when they are not actually fluent in that language. Linguist Veroboj Vildomec reported that a multilingual who spoke some Russian dreamed that he was speaking fluent Russian. But when he woke up, he realized that it had been in fact a mixture of Czech and Slovak, with a bit of Russian ..... and not fluent Russian after all.
You may think you can speak perfectly fine, but you might be dreaming about having fluency with your new language. Tricky eh? Thinking and dreaming are quite interrelated with this subject. Thinking with a new language means you are in a later stage in which the language intervenes while you are planning to speak and not surprisingly, your inner speech:
But then why do we believe we think in a specific language? This is because language intervenes at a later stage while planning to speak, just as it does in our inner speech. Temple University linguist, Aneta Pavlenko, defines the latter as subvocal or silent self-talk, that is mental activity that takes place in an identifiable linguistic code and which is directed primarily at the self.
Dreams "act" in the same way: you will soon be dreaming in that language. But this all depends on the situation at hand:
They were either basing themselves on the planning stage leading to overt speech (the stage Berkeley psycholinguist Dan Slobin calls "thinking for speaking") or on their inner speech. Their answer is not surprising, then, since bilinguals use their languages for different purposes, in different domains of life, with different people.
So to make this easier, let's use me as an example. If I am thinking about school, English will be used since I am in the United States of America. But at home, I will think in Vietnamese since that's the main language my family uses. So what language you use depends on the situation (and other factors) you are currently in. Speaking of other factors:
University of London linguist, Jean-Marc Dewaele, has examined the factors governing language choice in inner speech. Among them we find the language that is dominant, when and where the languages were acquired, the bilingual's proficiency in these languages, the frequency of language use, and the size of the speaker's social network.
The source used for the answer.
In my opinion you have to think in the target language before being able to dream in that language. And for me, if you think in the target language, you will dream inevitably in that language. The rest of the process will be acquired at high speed because your brain has decided to think in the target language rather than in your native language.
I sometimes dream that I or someone else is speaking a language that I'm learning, but then when I wake up and analyze it, I realize that it was mostly gibberish, with a word or two of the language thrown in, and those often used to mean something entirely different from what they actually mean. For example the time I dreamed that my radio was speaking Spanish, and then woke up and realized that "espejo" means "mirror", not "hairbrush" which it supposedly meant in my dream. I only recall one time where I dreamed I was speaking another language, and it held up to after-waking examination, and that was after I had already become fairly proficient.
As a person who learned many foreign languages, I dream in at least in 4 languages I use daily at work and in the family. Irrespective of my proficiency in these languages, I don't see something special in dreaming in them, as I am already at the level of fluency where I think directly in these languages (at least about simple things).
However, sometimes I dream about speaking other languages where I am not that proficient in. And I really enjoyed the feeling of freedom, being free of any reservation while speaking these languages in your dream. When, after I wake up, I try to remember and again feel the same freedom in the language and sometimes I manage again to experience this, this time already during a small talk or informal conversation and it helps me to consolidate my knowledge and boost my confidence with the language, without learning new grammar or vocabulary.