There are two numbering systems used to count things in Korean. There are Native Korean numbers and Sino-Korean numbers. Today we will talk about Native Korean numbers.
Numbers (1-90)
For numbers over 10, just add 1-9 to the end of the number. For example 29 is 스물아홉 (seu-mul a-hop).
0: 공/영 (gong / yeong)
1: 하나 (ha-na) *
2: 둘 (dul) *
3: 셋 (set) *
4: 넷 (net) *
5: 다섯 (da-seot)
6: 여섯 (yeo-seot)
7: 일곱 (il-gop)
8: 여닯 (yeo-dal)
9: 아홉 (a-hop)
10: 열 (yeol)
11: 열하나 (yeol-ha-na)
12: 열둘 (yeol-dul)
13: 열셋 (yeol-set)
14: 열넷 (yeol-net)
15: 열다섯 (yeol-da-seot)
16: 열여섯 (yeol-yeo-seot)
17: 열일곱 (yeol-il-gop)
18: 열여닯 (yeol-yeo-dal)
19: 열아홉 (yeol-ah-hop)
20: 스물 (seu-mul)
30: 서른 (seo-reun)
40: 마흔 (ma-heun)
50: 쉰 (swin)
60: 예순 (ye-sun)
70: 일흔 (il-heun)
80: 여든 (yeo-deun)
90: 아흔 (a-heun)
Numbers (100-1,000,000,000,000)
After 100, the numbering system switches over to the Sino Korean numbering system.
100: 백 (baek)
200: 이백 (i-baek)
300: 삼백 (sam-baek)
400: 사백 (sa-baek)
500: 오백 (o-baek)
600: 욕백 (yuk-baek)
700: 칠백 (chil-baek)
800: 팔백 (pal-baek)
900: 구백 (gu-baek)
1,000: 천 (cheon)
2,000: 이천 (i-cheon)
3,000: 삼천 (sam-cheon)
4,000: 사천 (sa-cheon)
5,000: 오천 (o-cheon)
6,000: 욕천 (yuk-cheon)
7,000: 칠천 (chil-cheon)
8,000: 팔천 (pal-cheon)
9,000: 구천 (gu-cheon)
10,000: 만 (man)
20,000: 이만 (i-man)
30,000: 삼만 (sam-man)
40,000: 사만 (sa-man)
50,000: 오만 (o-man)
60,000: 욕만 (yuk-man)
70,000: 칠만 (chil-man)
80,000: 팔만 (pal-man)
90,000: 구만 (gu-man)
100,000: 만 (sip-man)
1,000,000: 이만 (baek-man)
10,000,000: 삼만 (cheon-man)
100,000,000: 사만 (eok)
1,000,000,000,000: 만 (jo)
Larger numbers are divided in units of 10,000. Which in my mind, means I need even more math to count 😭
* When the numbers 하나, 둘, 셋, and 넷 are used with counters, they change into 한 (han), 두 (du), 세 (se), 네 (ne). For example:
쓰레기 봉투 세 개
(sseu-re-gi bong-tu se gae)
three trash bags
커피 두 잔
(keo-pi du jan)
two cups of coffee
Native Korean numbers are used for:
counting objects 
연필 다섯 개
(yeon-pil da-seot gae)
five pencils
people
여섯 명*
(yeo-seot myeong)
six people
*You would 분 use instead of 명 in the honorific form.
age
할머니는 아흔여닯 살이세요.
(hal-meo-ni-neun a-heun-yeo-dal sal-i-se-yo)
Grandma is 98 years old.
the hour in time
열한 시 오십구 분이에요.
(yeol-han-si o-sib-gu bun-i-e-yo)
It is 11:59.
duration of hours
그 아이들은 한 시간 동안 텔레비전을 봤어요.
(geu a-i-deul-eun han si-gan dong-an tel-le-bi-jeon-eul bwa-sseo-yo)
The kids watched television for one hour.
duration of months
그는 세 달 세계 일주를 여행했어요.*
(geu-neun se dal se-gye il-ju-reul yeo-hang-hae-sseo-yo)
He traveled around the world for 3 months.
*This can also be expressed with Sino-Korean numbers. Instead of 세 달 it would be described as 삼 개월.
animals
개가 여닯 마리 있어요.
(gae-ga yeo-dal ma-ri i-seo-yo)
There are 8 dogs.
academic subjects
저는 오늘 세 과묵이 있어요. 저는 역사 화학 수학 수업이 있어요.
(jeo-neun o-neul se gwa-mok-i i-sseo-yo. jeo-neun yeok-sa hwa-hak su-hak su-eob-i i-sseo-yo.)
I have three subjects today. I have History, Chemistry, and Math classes.
volumes
도서관에는 수백 관의 책이 있어요.
(do-seo-gwan-e-neun su-baek gwan-ui chae-gi i-sseo-yo)
There are hundreds of volumes of books in the library.
sheets of paper
종이 열두 장
(jong-i yeol-du jang)
twelve sheets of paper
bottles
다섯 병.
(da-seot byeong)
five bottles
cups and glasses
다섯 잔
(da-seot jan)
five glasses
times (instances)
그녀는 오늘 그 노래를 스물 다섯 번 들었어요.
(geu-nyeo-nun o-neul geu no-rae-reul seu-mul da-seot beon deu-leo-sseo-yo)
She listened to the song 25 times today.
vehicles
주차장에 차가 네 대 있어요.
(ju-cha-jang-e cha-ga ne dae i-sseo-yo)
There are four cars in the parking lot.
Ordinal Numbers
Ordinal numbers are just like Native Korean numbers with a little extra something on the end. So if you want to tell the position of something on a list (like first, second, third, fourth, and so on), you will use the ordinal numbers as such below:
1: 첫 뻔째 (cheot-bban-jjae)
2: 둘 뻔째 (dul-bban-jjae)
3: 셋 뻔째 (set-bban-jjae)
4: 넷 뻔째 (net-bban-jjae)
5: 다섯 뻔째 (da-seot-bban-jjae)
6: 여섯 뻔째 (yeo-seot-bban-jjae)
7: 일곱 뻔째 (il-gop-bban-jjae)
8: 여닯 뻔째 (yeo-dal-bban-jjae)
9: 아홉 뻔째 (a-hop-bban-jjae)
10: 열 뻔째 (yeol-bban-jjae)
11: 열하나 뻔째 (yeol-ha-na-bban-jjae)
12: 열둘 뻔째 (yeol-dul-bban-jjae)
13: 열셋 뻔째 (yeol-set-bban-jjae)
14: 열넷 뻔째 (yeol-net-bban-jjae)
15: 열다섯 뻔째 (yeol-da-seot-bban-jjae)
16: 열여섯 뻔째 (yeol-yeo-seot-bban-jjae)
17: 열일곱 뻔째 (yeol-il-gop-bban-jjae)
18: 열여닯 뻔째 (yeol-yeo-dal-bban-jjae)
19: 열아홉 뻔째 (yeol-ah-hop-bban-jjae)
20: 스물 뻔째 (seu-mul-bban-jjae)
30: 서른 뻔째 (seo-reun-bban-jjae)
40: 마흔 뻔째 (ma-heun-bban-jjae)
50: 쉰 뻔째 (swin-bban-jjae)
60: 예순 뻔째 (ye-sun-bban-jjae)
70: 일흔 뻔째 (il-heun-bban-jjae)
80: 여든 뻔째 (yeo-deun-bban-jjae)
90: 아흔 뻔째 (a-heun-bban-jjae)
100: 백 뻔째 (a-heun-bban-jjae)
So that’s it for native numbers and ordinal numbers! I don’t know about y’all, but that’s enough numbers for me for now!