Adding ~시

안녕하십시오, 안녕하십니까? 잘 하시네요?!

What the hell does 시 means?! 

To make a the long idea short, you add 시 when the person you are talking about deserves respect.

I was confused too... I thought adding 요 and ~ㅂ니다 is all you need to show respect.

The thing is, you use 시 when the person you are talking about deserves the respect.

for example you want to say that your father went home already
You add (으)시 to the stem of the verb/adjectives

우리 아버지는 집에 이미 갔어요. 

Even though you have put 요 This will be rude to say. You will want to give respect to your father by putting 시

우리 아버지는 집에 이미 가셨어요.
가다 => 가시다 
갔다=> 가셨다 

more example

형이 저한테 한국어를 가르치주셨어요. 형 Taught me Korean.
잘하시네요! - You did well! same meaning with (잘하네) but a lot more polite.

Note: I have highlighted this and mentioned this a lot but you only use 시 when talking to a person that deserves respect. You dont use 시 when you talk about yourself.

저는 어제 학교에 가셨어요 - This would be wrong since you are talking about yourself.

저는 어제 학교에 갔어요 -  I went to school yesterday.

~(으)십시오 is like ~(으)세요, It is commonly in Imperative way of speaking.

as you can see 십시오 is more polite than 세요 (although 세요 is already polite)

가! Go!

가세요! Please Go!

가십시오! Please Go! ( more polite)

Now that you know the concept I'm going to introduce the things I have learned from random chatting apps ( yes I used random chatting apps aha)

Usually the first thing they almost ask you is:

한국분이세요? 

몇살이세요?

여자분이세요?

no they are not asking you to be Korean, it is the 시 principle

normally this would be ok 한국분이에요? but to be polite you add the 시 after the 이다
시 can be added to 이다, it is really polite, and I talk in this way too. especially to strangers.

한국분이다 => 한국분이시다 

한국분이야 => 한국분이셔 

한국분이에요=> 한국분이세요

한국분입니까?=>한국분이십니까?

It basically makes the statement more polite.

Oh yeah 셔 can be used if you are talking to somebody your age, and you are talking about someone that deserves respect. It would be Informal, but it is polite.

니네 아버지께서 키가 크셔 - Your father is tall
You should not use these to strangers for they might get mad at you 니네 is still 반말 look for the polite words below.

Hey wait. That's not all..
In Korean If you are talking about a person that deserves respect. You don't just add 시. There are some words that will transform to be more polite.
here are the words/particles that will transform

우리 = 저희
Although 우리 is usually alright, you should use 저희 when talking to someone higher than you.
'우리나라'  is commonly used though
"things referred by 우리 instead of 내"  나라(country), 보모님 (parents), 학교(school),오빠/형, 누나/언니 (siblings)
너의 = 너희(니네) 
When you are talking to your friend's "things referred by 우리 instead of 내"  you should use 너희 instead of 너의. this is still 반말, don't use it to older peoples or stranger.
~는/~가/~이 = 께서(는)
This is the subject marker, when someone really higher than you did an action, you must not refer to him as 는/이/가
To address somebody's parents this would be fine : 님의 어머니께서 미인이시네요. You mother is Beautiful.
말하다= 말씀하다 , 말 = 말씀 
you still have to add 시 to the 하다. 말씀하시다 
주다 = 드리다 
엄마가 선물 드렸어요. My mom gave a present,
선생님께 말씀드릴거예요. I talked to the teacher. (Yes the 해줘 will be 해드려)
선생님은 저한테 가르쳐주셨어요. The teacher Taught me.
주시다?? .. Ok 주시다 can be acceptable if: Something, did something for you.
and 드리다 if you have done something for someone higher than you.
~에게 = ~께 
선생님꼐 말씀하실게요. I will say it to the teacher. 
선생님께 말씀해주실 거에요 (although the first one was grammatically acceptable this is more natural to say)
자다 = 주무시다
These phrases are commonly heard
주무세요~ (주무시다 + 요)
안녕히 주무세요~ (안녕 (安寧)actually means peace literally, or to be well) but we are not here to talk about the 
안녕 phrases.
있다 = 계시다 
Yes you change every 있다 to 계시다 
가고 있다 = 가고 계시다
할아버지께서 서울에서 계시다 = Grandfather is in Seoul
I dont think you have to say 계시다 if you talk about things though. you dont need to respect things
And then there is the 안녕 phrase again
안녕히 계세요
Right, this is usually said when the person is staying and you are leaving, is it's like ( Please stay well? literally) but please just think of it just as "Goodbye"

(읍)ㅂ시다 is just like ~자 , it makes the meaning of "let's" 
갑시다! 가자! 

I guess that's everything I have to talk about. I was surprised too that ㅂ니다 wasnt enough
it might be Formal but it is not always polite. 시다 must be added