Note: Examples are formatted "Roman Numbers - Kanji - Katakana"
Note: ...Yeah, this works alot like roman numerals, but, since the rules are different, I recommend keeping them separate.
While Japanese can use Roman Numbers like English, natively, there is a word and a different set of symbols to represent each number.
1-10
Like English, numbers 1 through 9 are represented by a single character. It IS still a base 10 system, but there is no kanji for 0. Instead, there is a kanji for 10.
1 - 一 - いち
2 - 二 - に
3 - 三 - さん
4 - 四 - し
5 - 五 - ご
6 - 六 - ろく
7 - 七 - しち・なな
8 - 八 - はち
9 - 九 - きゅう
10 - 十 - じゅう
11-19
At 11, you start combining symbols. 10 + 1 is 11. 十 + 一 is 十一.
11 - 十一 - じゅういち
12 - 十二 - じゅうに
13 - 十三 - じゅうさん
14 - 十四 - じゅうし
15 - 十五 - じゅうご
16 - 十六 - じゅうろく
17 - 十七 - じゅうしち
18 - 十八 - じゅうはち
19 - 十九 - じゅうきゅう
Tens (20, 30, etc)
Here it's a combination of 2 and 3 characters.
For the tens (20, 30, etc) put a character for 1-9 in front of 10. (I.E 二十 for 20, 三十 for 30).
Inbetween numbers work just like "11-19" above (I.E. 二十一 for 21, 三十一 for 31).
20 - 二十 - にじゅう
30 - 三十 - さんじゅう
40 - 四十 - しじゅう
50 - 五十 - ごじゅう
60 - 六十 - ろくじゅう
70 - 七十 - しちじゅう・ななじゅう
80 - 八十 - はちじゅう
90 - 九十 - きゅうじゅう
100 & Beyond
The remaining symbols (for this lesson) are 100 = 百, 1,000 = 千, and 10,000 = 一万.
They follow the exact same stacking pattern.
100 is just 100
百 - ひゃく
101 is 100-1
百一 - ひゃくいち
111 is 100-10-1
百十一 - ひゃくじゅういち
120 is 100-2-10
百二十 - ひゃくにじゅう
121 is 100-2-10-1
百二十一 - ひゃくにじゅういち
200 is 2-100
二百 - にひゃく
201 is 2-100-1
二百一 - にひゃくいち
211 is 2-100-10-1
二百十一 - にひゃくじゅういち
220 is 2-100-2-10
二百二十 - にひゃくにじゅう
221 is 2-100-2-10-1
二百二十一 - にひゃくにじゅういち
Same for 1,000.
1,000 - 千 - せん
1,001 - 千一 - せんいち
2,000 - 二千 - にせん
And 10,000.
10,000 - 万 - まん
10,001 - 万一 - まんいち
20,000 - 二万 - にまん