"내가 보고 싶었구나" is same with bellow because the subject can be omitted. = (너는) 내가 보고 싶었구나. or (너가=네가) 내가 보고 싶었구나. It means (you) missed me. 1. '-이/가' can be used like indicating object because an topic marker and an object marker can be used in one sentence. And two subject markers also can be used in one sentence in Korean. For example... (나는) 너가(=네가) 보고 싶어. / (저는) ~ 씨가 보고 싶어요. ( I miss you.) ~ 씨가 ~가 좋다고 했어요. (~ 씨 said that she/he likes ~.) (너는) 내가 보고 싶었구나. Or (너가=네가) 내가 보고 싶었구나. (You) missed me. * 너는 and 너가 are usually omitted. * 네가 is same with 너가(네가 is a writing form and 너가 is a speaking form). 2. '보고 싶다' means to miss, to want to see. In '(나는) 친구가 보고 싶다', it means 'to miss' (I miss my friend). '-고 싶다' is used with '-이/가' rather than '-을/를'. (1) (나는) 내 친구가 보고 싶다. (나는) 비빔밥이 먹고 싶다. (2) (나는) 내 친구를 보고 싶다. (나는) 비빔밥을 먹고 싶다. --> (1) is more natural than (2). * '을/를' can be used more naturally this way. 너는 나를 보고 싶어했다. (You missed me.) 내 친구는 나를 보고 싶어했다. (My friend missed me.) 3. '-구나' is used when someone found something newly at that moment (and a little surprised). (너는) 내가 보고 싶었구나. It means '(You) missed me' and implies the speaker found it at that moment (and slightly surprised).

V(transitional verb)+고 싶다 is very special pattern. With focusing on the verb, It is preceded by 을/를 With focusing on 고 싶다, It is preceded by 이/가 In this case, You can regard it as an adjective like 좋다, 싫다, 없다, 있다 where it has meaning of "wanting to do something". 나는 사과가 좋다 : For me, there is an apple that I like = I like an apple. 나는 사과가 먹고 싶다 : For me, there is an apple that I'm wanting to eat => I want to eat an apple. Following both have same meaning. 너는 내가 보고 싶었다 : For you, there is me whom you were wanting to see. => You wanted to see me. 너는 나를 보고 싶었다 : You wanted to see me.