For the first person "I", there is 나 (ordinary use) and 저 (lowers oneself to show the other person respect).
These two have different forms depending on how it's used in a sentence.
- 나는(난)/저는(전), 내가/제가 => as the subject. (나는 행복해 = I am happy; 내가 할게 = I'll do it)
- 나를(날)/저를(절) => as the object of a verb. (나를 밀지 마 = do not push me)
- 나의(내)/저의(제) => possessive case. (내 책 = my book)
The second person "you" has 너 which is only used between close friends or when talking to children.
- 너는(넌), 네가 => subject. (너는 학생이다 = You are a student; 네가 해 = You do it)
- 너를(널) => object. (너를 못 믿겠어 = I can't trust you)
- 너의(네) => possessive. (네 자전거를 나한테 빌려 줄래? = Would you lend me your bicycle?)
There is no convenient second person pronoun that can be used for adults in general like "you" in English, because Koreans use the person's title or name most of the time. 당신 is only used in certain limited contexts of writing(letters and literary works). People don't normally call others 당신 because it sounds rude. Some entry level textbooks use 당신 only because there is no word for "you".
Korean pronouns can get complex because they not only change with their role in the sentence as well as the politeness level and other contextual elements, but often have multiple forms owing to contraction and sometimes for pronunciation-related reasons.
Most grammar books and sites should have all of them explained with examples.