とてもis used for affirmative, and あまりis used for negative sentences.
あの映画はとてもおもしろかった。
このお菓子はあまりおいしくない。
あの子はとても優しい。
あの服はあまり私の好みではない。
As for the sentence that you mentioned, "最近はあまりおいしいと思わなくなりました。"
he's saying that he doesn't think that tastes as good as he used to think anymore lately, which is a negative sentence.
I imagine it's very complicated till you get used to using those words.
Hope this explanation helps!