The system of Japanese numerals are just the same as those of the Chinese numerals since both uses Chinese characters. The only notable difference is the Japanese pronunciation. Also, instead of using Chinese characters, they often opt to just use the Arabic system.
The numerals are based on decimal (base-10) and are grouped in ten thousands (compare to our grouping of thousands).
The first ten numerals are 1. 一 (ichi), 2. 二 (ni), 3. 三 (san), 4. 四 (yon), 5. 五 (go), 6. 六 (roku), 7. 七 (nana), 8. 八 (hachi), 9. 九 (kyuu) and 10. 十 (juu). After ten, the characters (or groups of characters) are "added" to get the value. This is similar to our system: "twenty-one = twenty + one", "sixty-five = sixty + five". 十 (juu) = ten, to get the other multiples of ten, simply precede it with the corresponding character, this acts as a "multiplier" to ten.
- 二十 (ni juu) = 2 * 10 = 20
- 三十 (san juu) = 3 * 10 = 30
- 二十一 (ni juu ichi) = (2 * 10) "twenty" + 1 = 21
- 六十五 (roku juu go) = (6 * 10) "sixty" + 5 = 65
The same is applied to the other powers of ten, any "digit" character preceding the character for the power of ten would act as a "multiplier". This is similar to our place values.
See Wikipedia:Japanese numerals for more info.