도 cannot occur with the subject marker 이/가 or the object marker 을/를 - if 도 is used to mark the subject or object it must replace rather than occur alongside these markers/particles. 도 can be said to have the basic meaning: 'too', 'also', 'as well'.
이것은 한국 제품이에요. 저것도 한국 제품이에요. (This is a Korean product. That is a Korean product too.)
어제 포장마차에서 술을 마셨어요. 노래방에서도 마셨고요. (Yesterday I drank alcohol at the drinking stall. And I drank at karaoke too.)
오늘 인호하고 영화를 보고 저녁도 먹었어요. (Today I saw a movie with Inho and ate dinner too.)
공부하기도 해요. (I'm studying too.)
As can be seen in the examples above, wheras corresponding English words such as 'too' and 'as well' tend to occur at the end of the sentence, the Korean 도 must always attach to the thing which is being stated in addition.
도 is also used in negative sentences, where English would use 'either' instead:
이것은 수입품이 아니에요. 저것도 수입품이 아니에요. (This isn't an import. That isn't an import either.)
시간이 없어서 우체국에 못 갔어요. 은행에도 못 갔고요. (I was out of time, so I wasn't able to go to the post office. I wasn't able to go to the bank either.)
In it's 'too', 'also', 'as well' function, 도 often occurs twice in a sentence. This shows a kind of tandem agreement between noun phrases meaning 'both ~ and ~' (or 'neither ~ nor ~' in negative sentences:
아침에도 밤에도 일해요. (I work both in the morning and at night.)
인호는 친구도 적도 아니에요. (Inho is neither a friend nor an enemy.)
도 may also appear twice in a sentence with two clauses(which are typically linked with '-고') in the meaning of 'both ~ and ~ too'(or 'neither ~ nor ~ either' in negative sentences):
학생도 있고 직장인도 있어요. (There are both students and there are workers too.)
그 술집은 술 값도 싸고 분위기도좋아요. (At that pub, the price is both cheap and the atmosphere is good too.)
<참고> Jaehoon Yeon and Lucien Brown(2011), Korean: A comprehensive Grammar, 146-148.