나 and 저 both mean ‘I’ or ‘me’. 저 is a humble way to say 나. When you talk to a person who is older or higher position than you or stranger, you have to use 저. On the other hand, 나 is used for friends(the same age) or a person who is younger than you. Therefore 나 is often used with casual endings which is 아/어/여 or ㄴ/는다 while 저 is often used with polite endings such as -아/어/여요 or -(스)ㅂ니다.
나 and 저 are often used with particles like 이/가(subject particles), 을/를(object particles), 한테(to), 하고(with/and). For example,
나+가 => 내가(it is not 나가)
저+가 => 제가 (it is not 저가)
나+를 => 나를
저+를 => 저를
나+한테 => 나한테
저+한테 => 저한테
나+하고 => 나하고
저+하고 => 저하고
Sentence>
내가 먹었어.
제가 먹었어요.
그 사람이 나를 좋아한다.
그 사람이 저를 좋아합니다.
나한테 줘.
저한테 주세요.
나하고 가자.
저하고 가요.
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