For example, it is not unusual in international cities like London, NYC, Paris, etc., for parents from, say, China, to move to NYC with a baby and have the child eventually attend (American) pre-school. They will then have a nanny from Sweden or Poland or Puerto Rico. The child will be able to converse in Mandarin, Swedish and English and not miss a beat. Astounding--I have seen it several times myself.
The secret to success in a second language is when one begins to think in that language rather than thinking in English then mentally translating it before speaking. Unfortunately, I've never gotten this far. There are some super-familiar Biblical phrases I understand without translating (Vaydabber HaShem 'el Mosheh le'mor: And HaShem spoke to Moses saying), but when it comes to the modern spoken language I have to spend thirty minutes figuring out how to translate the English into Hebrew and then speak it very carefully--and even then I usually make a mistake of some kind. And I've been studying Biblical Hebrew for 27 years!
Unfortunately there's very little commonality between learning a textual and a spoken language.
Maybe I should try learning Old English instead?