Um, with all due respect, there seems to be quite a bit of inaccurate information in this thread.
In the United States, deals can be done for a number of different territories. For example, I can sell World rights, all languages, to a publisher. In that case, the publisher, not the author, controls those rights and will market them to foreign publishers, generally through their subsidiary rights department and a network of foreign literary agents who represent US publishers and agents in their home countries.
I can sell just World English rights, in which case the author controls the translation rights and I, as the agent, will market those rights to foreign publishers through my network of foreign co-agents who are literary agents in their foreign countries.
I can sell just US, Canadian and non-exclusive Open Market rights, in which case I would market UK rights myself directly to UK publishers, and translation rights as above.
The foreign publishers have English-speaking editors who read US-published books and decide to acquire them. The foreign publisher then arranges for translation for their edition.
In the US, there are shockingly few bilingual editors who read foreign books and look for those to translate into the US. Thus, there are a few houses who specialize in this, including Kodansha, which brings a lot of Japanese works here, and some literary imprints of larger houses that do works in translation from Spanish or other languages. Since translating a book from another language is expensive, and since there are so many books already in English available, a book needs to be quite exceptional to warrant a US publisher paying to translate it.
In some cases, a foreign publisher who thinks they have something exceptional will pay one of the translators they use for translating from English to translate a book into English, or just a few chapters. They then shop these books in the US via their rights person or a US literary agent.
That said, the US publishers that regularly do works in translation usually have a foreign-language speaker on staff or a free-lance reader who can read the books in their native languages and do a reader's report.
I think if you wanted to become a translator of, say, Japanese books to English, you should probably contact someone at Kodansha and ask them their requirements. I suspect they have a test of some kind they would want you to complete, assuming they are looking for new translators.
If you found a book in, say, Greek, that you thought was amazing and should be published in the US, you have a couple of choices that I see:
1. Contact the Greek publisher and ask who controls English-language rights. Contact that person (or publisher) and say that you are interested in translating the work into English and volunteer to translate a few chapters for their review. If they like them, they can shop them to US publishers with the translating a part of the deal and, if it sells, you get the gig, hopefully.
2. Contact a US publisher you think may be the right one for the book and send them the book and your sample translation and tell them you know who controls the rights and if they acquire those rights you'd like to be considered for the translation.
Option one is likely the best bet, IMHO.
Z