Basically, when you want to become a book translator, you have to know at least one more language besides your own. Seems simple, but that isn’t always so.
In the USA, not every citizen will speak French, or German. Some will know a bit of Spanish. In Europe, the situation is different. In countries as my own (Belgium) people are speaking a language that only covers a small territory, and thus they are forced to learn more languages. In Belgium, especially Flanders, each school-going child learns French, English, and most of them also study German and Spanish.
You must also realize that the need for book translators in the USA will not be too big. Few books will be translated into English. A few literary novels, whose authors have gained world acclaim, will need to be translated. In Europe, most novels that are published come from either the UK or the USA, so the chances of finding work there are bigger.
There is also a difference between the USA and Europe which concerns qualifications. As far as my knowledge goes, there are absolutely no qualifications asked when you want to become a book translator in the USA. In most European countries, including my own, you need to have a master’s in either literature/linguistics or translator/interpreter. Both degrees require a study of 5 years before getting the diploma.
Of course, a university degree is not always a key to success. In my experience, the best way to learn a language is to spend time in the country where it is spoken and have lots of contacts with native speakers. This may perhaps require another year. As a student, I spent one year in the USA after finishing high school in my home town. The same goes for my knowledge of German. I did study it at school, but only learned it better by spending four years in Germany where I also worked as a teacher.
Once you have the necessary qualifications (which you can also get by attending evening courses, or open university, or even online courses) you can try to find work. There are many publishing houses around the world, so one of your first tasks should be to check their website and see if they have any vacancies. When they have, you can apply for the job.
What you should also be aware of, is the fact that book translators are poorly paid. Literary translations are among the lowest-paid professions known to economic science. If literary translators were employees rather than freelancers, their pay scales would be illegal!
So my advice is not restrict yourself to book translations only, if you want to make it as a freelancer. Take on as much work as you can elsewhere, to give you more credibility. This will certainly help if applying for a job at another publisher’s.
Also pay attention to the rates you set. They can’t be too low, and equally not too high. Lots of beginners make basic business mistakes and don’t know how to market themselves. But rest assured, there are courses to learn how to do this.