None of your sentences are wrong, Sonia. But the final sentence has a different meaning to the other three. It implies (suggests) that you expected him to be shy but, in fact, he wasn't. Sentences one and three are both correct and they both mean exactly the same thing. However, for these two sentences, I think the simple past tense of the verb "to find," (found) would be better than the simple past tense of the verb to think (thought). Sentence two could mean the same thing as sentences one and three or could mean the same thing as sentence four..

The first one (I thought him shy) is the only incorrect one in terms of grammar - this may just be as a speaker of American English, or my variety of American English but I don't think it is commonly used. I thought he was shy = the best option if you are speaking in the past tense (i.e.: you thought he was shy when you met him earlier) I thought him to be shy = means the same thing as the one above, and I think this is technically grammatically acceptable, but it is not a commonly used structure day-to-day I thought he would be shy = "would be" signifies that he wasn't actually shy, so it may not be the meaning you're looking for in this context, but it is still grammatically correct