hd5467's comment is mostly correct.
Here's 4 different usages for '당신'.
1. when you refer the person in front of you
It is usually rude to use '당신' in this case even to someone around my age or younger.
e.g., 당신 뭐하는 사람이야? 당신 똑바로 해
2. '당신' can be used between married couple.
e.g., '당신 저녁식사 했어요?' = 'Did you have dinner?"
This usage is common in both real life and dramas.
3. In songs or literatures, '당신' is not rude, and sometimes somewhat poetic.
In this case, the other person is usually not in front of you.
e.g., 당신은 어디에 계시나요 (where are you, my darling)
4. sometimes it refers not 'you' but 3rd person.
할아버지께서는 당신의 손주들을 사랑하셨다 (My grandfather loved his grandchilden)
in this example, '당신' = 'his'.
'당신' is used when we refer the same person again in the same sentence.
And usually the person is senior than me in this case.
Among above usages, 1 is rude, and 2,3,4 is not rude at all.
Also, 1,2,3 is quite common, but you'll rarely see 4, so don't worry about 4.
As hd5467 said, pronouns can be dropped a lot in korean.
It is ok because we can infer who is the subject or the object.
e.g, "이 책 줄께" = "(I'll) give (you) this book"
So either you can drop 'you', or if it is ambiguous, you can call the person first, and drop the pronoun 'you'.
e.g., 아빠, 주무세요? = Dad, (are you) sleeping?