my nephew spoke english from watching cartoons, initially from kiddie cd's that his grandmother bought, and then later on from disney channel, nickelodeon, national geographic, discovery kids, etc. (yun lang, hindi kami pumapayag sa mga tagalized English cartoons, but this is for another topic)
we talk to him in English when he asks in English or if the conversation is in English, this is to correct grammar, for better sentence construction, and especially to broaden his vocabulary.
on the other hand, we talk to him in Filipino if the conversation is in Filipino for the same reasons as above, pero mostly for vocabulary, dahil madali naman ang grasp natin sa Filipino and madali mag-construct ng sentence, hindi lang madali mag-translate ng tagalog terms pag first time nya naririnig.
eventually, he became more comfortable with speaking English. so now he is speaking in English 60% to 70% of the time, Filipino fluently mga 20% of the time and then we translate deeper Filipino words that he doesn't know the meaning of. we did not choose this for him nor do we encourage/discourage either language, kung baga, kung saan sha comfortable. hindi lang kami pumapayag pag hinahalo nya ang English and Filipino sa isang sentence, o kaya pag sinisingit nya isang Filipino word sa gitna ng English na sentence (ex. that is so liit).
downside lang nito, we have to remind him to speak Filipino when he is with his playmates, pero wala naman problema dito dahil kaya naman nya.
i have no problem with him sounding like a Filipino speaking English, basta tama ang sentence construction, tama ang grammar, may sense naman, walang omitted words.
and last na sis, with regard to teaching him anything specific, when he was younger, we just took our cue from him, when we saw na he was ready to advance to reading a kiddie thesaurus, we bought him one; when we saw na he was trying to speak English but his past tense was wrong, dun kami nagtuturo ng tamang past tense ng mga words, or tamang use ng articles. = )