My Russian teacher tell me that this two verbs учить and изучить means study, but when I need to use учить and when изучить? учить means also learn?
There are two nuances.
First, "учить" can mean both "study" and "teach".
Я учу математику (study)
Я учу ученика (teach)
Second, "изучить" often has the connotation "to study completely".
Я учил это очень долго и наконец-то изучил полностью.
(I studied this topic for a long time, and eventually had studied it completely)
Изучить is also to research. And to learn by heart or learn very well is выучить.
Студент изучил новые слова. - The student has studied new words, he has made a research and come to some conclusions on them.
Студент выучил новые слова. - The student has learned new words, and now he can use them in speech.
Студент учил новые слова. - The student learned new words, or he was learning the new words when sth. happened.
Usually students who haven't learned the words say: "Я учил." - "Вы выучили?" - "Я учил." )))))