Hello~ I decided to continue this "series" hehe. So this is the second part: words & phrases. 
I wasn't sure what kind of phrases would be useful besides the everyday greetings and common questions... So you should let me know which to add ^o^
Hope this helps~ And hopefully you can read these in Korean! But I provided the romanization anyway. I use my own unstandardized version of romanization, whichever spelling I think helps read it most accurately - so it may differ from what you see in other places!

*Formal and Informal speech is very important, so make sure they're used in the proper context.
You would never use informal speech with your elders, boss, teachers, etc. (Family is OK sometimes. I only use informal speech with my mom, personally - not with my father or my grandparents/aunts/uncles/etc, but it differs per family!)

*Lit. means literal translation. 

*X means any object.

FORMAL

Hello: 안녕하세요?
Ahn-nyeong-ha-seh-yo
Lit. Are you at peace? / Stay in peace

Good Night. 안녕히 주무세요.
Ahn-nyeon-hee ju-mu-seh-yo

Yes/No: 네/아니요.
Neh/Aniyo

What is (it)?: 뭐에요?
Mwoh-yeh-yo?

Where is X?: X 어디에 있어요?
X Uh-di-eh iss-uh-yo?

Why?: 왜요?
Weh-yo?

I’m/It’s okay : 괜찮아요.
Gwen-cha-na-yo.
Also used for rejecting an offer: “No, I’m/it’s okay”

I am looking for X… : X 찾고있느데요…
X Chat-go-eet-neun-deh-yo...

Excuse me…: 저기요…
Jeo-gi-yeo...
(lit. pronunciation is jeogiyo but no one says it like that colloquially)
used for getting someone’s attention

Excuse me (for being rude): 실례하겠습니다
Shil-leh-ha-gae-seum-ni-da
used when coming in/leaving a space

I’m sorry: 죄송합니다
Jwae-song-ham-ni-da

Also: 잘못했습니다
Jahl-mot-haess-seum-ni-da
Lit. I did wrong.

I am…: 저는…
Jeo-neun...

Thank you: 고맙습니다 / 감사합니다
Go-map-seum-ni-da / Gahm-sa-ham-ni-da
the latter is even more formal

I like X: X 좋아해요.
X Jo-wah-hae-yo
Just 좋아요 (without X) "jo-wah-yo" can mean various things like: That sounds like a good idea (let's do it), I like something you are referring to in conversation)

I hate X: X 싫어해요.
X Shi-reo-hae-yo
Just 싫어요 (without X) "shi-reo-yo" can mean various things like: I don't want to (do something), I don't like: to do something, something you are referring to in conversation)

It is X: X 이에요/예요
X ee-yeh-yo / yeh-yo.
The variation depends on if the word before it ends it a hard consonant sound or open vowel sound.
eg: (She) is my mom: 엄마예요. (마 is open vowel)
(He/She) is a/my teacher: 선생님이에요. (님 is closed consonant)

INFORMAL

Hello: 안녕.
Ahn-nyeong.

Goodnight: 잘자
Jahl-ja.

Yes/No: 응/아니
Eung/Ah-ni.

What is (it)?: 뭐야?
Mwuh-ya.

What?: 뭐?
Mweo?

Where?: 어디?
Uh-di?

Why: 왜?
Weh?

I’m/It’s okay: 괜찮아.
Gwen-cha-na.
Also used for rejecting an offer: “No, I’m/it’s okay”

Excuse me: 저기…
Jeo-gi...
used for getting someone’s attention

I’m sorry: 미안.
Mi-ahn.

I am…: 나는…
Na-neun...

Thank you: 고마워.
Go-ma-weo.

I like X: X 좋아.
X Jo-wah.

I hate X: X 싫어.
X Shi-reo.

It is X: X 이야/야. 
X ee-ya / ya.
variation depends on if the word before it ends it a hard consonant sound or open vowel sound
eg: (She) is my mom: 엄마야. (마 is open vowel)
(He/She) is a/my teacher: 선생님이야. (님 is closed consonant)

There are different ways to express the same sentence in Korean, especially with formal speech.
You can say X 좋아해요 "jo-wah-hae-yo" and X 좋아합니다 "jo-wah-ham-nida" - and they both mean "I like X."
The second version is somewhat more formal than the first, but I didn't really include most of the phrases in the second version because they're not used colloquially much.
& I hope you can see the pattern between how formal (usually) changes to informal!

VOCABULARY

Family: 가족
Ga-johk

Dad: 아빠 (formal: 아버지)
Ap-ppa / Abeoji
*It's spelled A-PPA, but if you say it out loud, the pronunciation is actually AP (lips close) - PPA/BBA.

Mom: 엄마 (formal: 어머니)
Um-ma / Uh-muh-ni

Younger sibling: 동생
Dong-seng

(if you’re a boy)
Older Brother: 형
Hyung

Older Sister: 누나
Noo-na

(if you’re a girl)
Older Brother: 오빠
Ohp-ppa

Older Sister: 언니
Uhn-ni

Boss (of the business* you work in): 사장님 
Sa-jang-nim
*it could be a very small business or. a huge company - doesn't matter.

Teacher: 선생님
Seon-seng-nim

Professor: 교수님
Gyo-su-nim

Home/House: 집
Jip

Bathroom: 화장실
Hwa-jang-sil

Store: 가게
Ga-gae

School: 학교
Hak-gyo

Elementary School: 초등학교
Cho-deung-hak-gyo

Middle School: 중학교
Joong-hak-gyo

High School: 고등학교
Go-deung-hak-gyo

College/University: 대학교
Dae-hak-gyo

Classes: 수업
Su-uhp

Hospital: 병원
Byeong-won

Restaurant: 식당
Shik-dang
*Most Koreans also understand if you say 'Reh-su-to-rang'

NUMBERS
There are two ways to count in Korean (Sino/Native). Sino has Chinese roots, while Native is ... well, Native (haha). You use certain ones when counting different things - and to know when to use what is all memorization (boooo, I know).

SINO (1-10)

일 il
이 ee
삼 sahm
사 sah
오 oh (pronounce it shortly - it's not as long as saying "Oh" in english.)
육 yook
칠 chil
팔 pahl
구 gu
십 shib

Counting past ten is easy! It's like adding.
So eleven would be 십일 shib-il and twelve 십이 shib-ee, and so on.
And for twenty is 이십 ee-shib and thirty 삼십 sahm-shib, and so on.

Some uses for these numbers are when you tell time (minutes only), naming months, what # day it is of the month, floors (of buildings), and other things.
Month is 월 "Weol": So January (first month) is 일월, pronunciation is ee-rweol, even though it's spelled il-weol*. February is 이월 ee-weol, and so on for the other months.
*** special case: JUNE & OCTOBER: it is not 육월 - it is 유월 yoo-weol, and it is not 십월 - it is 시월 shi-weol.

Day is 일 "il" (same pronunciation as sino '1'). So first day of the month is 일일, pronunciation is i-ril, even though it's spelled il-il*. And second day is 이일 ee-il, and so forth.

* the reason why it's not pronounced the way it's spelled is because 월 and 일 begin with the empty vowel ㅇ. And when the preceding syllable has a closed consonant sound like 일, 삼, 육, 칠, 팔, 십, the ㅇ takes on the sound of the closing consonant. 

Now you should be able to say dates!
For example:
January 26th is 일월 이십육일. i-rweol ee-shib-yoo-gil.
October 30th is 시월 삼십일: shi-weol sahm-shi-bil.

NATIVE (1-10)

하나 Ha-na
둘 Dool
셋 Seht
넷 Neht
다섯 Da-suht
여섯 Yuh-suht
일곱 il-gohp
여덟 Yuh-duhl
아홉 Ah-hohp
열 Yuhl

Multiples of Ten (20-90)
it's not as easy as sino, unfortunately

스물 seu-mool
서른 suh-reun
마은 mah-eun
쉰 shween (looks weird, I know)
예순 yeh-soon
일흔 il-heun
여든 yuh-deun
아흔 ah-heun
 

Counting in between isn't too difficult: It's like adding also.
so eleven is 열하나 yuhl-ha-na. and twelve is 열둘 yuhl-dool.
twentyfive is 스물다섯 seu-mool-da-suht, and so on.

After 90 - both Sino/Native merge to just one set of numbers! 

100 백
1000 천
10,000 만
100,000 십만 
1,000,000 백만
10,000,000 천만
100,000,000 (일)억 *
Even though 억 alone means 100 million, the 일 (sino 1) is added in front. This is not the case for 1000 or 10,000

and notice that 100,000 is 십만 = 10 x 10,000. and 1 million is 백만: 100 x 10,000. Easy multiplication!

We use the native counting system for things like counting people, things (objects), animals, time (hours only), and of course other things.
For time, hour is 시 'shi' and minute is 분 'boon' (try pronouncing boon shortly, not a long booooon like in English)
So we use native for hour (시) and sino for minute (분)
Unfortunately, the some native numbers go under a sort of a change when you actually use them to count things ...

the first four (1-4) change to:
한 hahn
두 du
세 seh
네 neh 
and the rest (5-10) are the same!
The number 20 also changes (I know, annoying) to 스무 seu-moo instead of 스물 seu-mool...

So now you should be able to tell time in Korean!
For example: 1:45 would be 한시 사십오분. hahn-shi sah-shib-oh-boon.
You must say 시 and 분! It's not like English where you can just say the numbers.

There is no 20 o'clock, but let's say you wanted to say "Twenty people"...
The counter for people is 명 'myung'. (*There are different counters for different things! You cannot use 명 for objects or animals)
It would NOT be 스물명 - it would be 스무명. 

*About the counters, there are different counters for objects, sheets (of paper), cars, people, animals, trees ... so many ... It , really... Once again, also memorization.
And when you are counting - you must must must always have the counter follow afterwards.
If someone asks you "How many people are there?" You cannot answer "One," or "Twentyfive" like you do in English. You must answer with 명 following after the number, even though it is understood you are talking about people...

Ah, so numbers were probably a little hard to grasp, and made this blog post a lot longer than I planned to make it...
I hope it made sense, and I hope you can now say dates & time! ^o^

I also hope that you guys tell me what other phrases / words to add onto the list for common/popular things that people want to know how to say!

Hope this helped~ ^o^

-- exoism