You use naega 내가 when you are referring to yourself in the sentence, kind of like 'I am'. Nae 내 means 'I', it's used only with the topic marker ga 가. For example, if you say "I am going to the store." you would say Naega gagey ey ga 내가 가게에 가.
Na 나 is used in a situation where the speaker is the subject or object of the sentence. It's always used with the subject marker nuun 는 (or object marker reul 를, I'll get to that). If I said, "I don't like football." I would say Na nuun 나는 (usually in colloquial it's contracted to 'Nan 난') chukguga shiro. 난 축구가 싫어. (Sometimes in colloquial Korean the subject '나' is left out of a sentence like this, as well as the topic marker 가 and you could just say 'Nan chukgu shiro or chukgu shiro.)
Reul (를) is the object marker, so you would use Nareul 나를 as we use 'me' in a sentence . If you want to say, ''Yuna Kim loves me." you would say Kim Yunaga nareul saranghae 김연아가 나를 사랑해.
Just want to explain more so you won't be misunderstood if you are talking to a Korean person ^^ because in Korea you have to be careful in your speech ;D it shows how mannered you are ^^
nae/na 내/나 are used in very informal speech (ban mal 반말). As a general rule, be careful when using ban mal and all forms of the word 'you' (ney,ni,no,dangshin 네,니,너,당신). It's only ok if you are talking to children, close friends of the same age or younger, family (but never older people) or your lover.