The Chinese numbering-system was one of the first things that came out of the Chinese character system about four millenia ago. They looked a bit different then, the system was standardized around 200 BC by the Qin Dynasty emperor Qin Shihuangdi. Note the huge number of Chinese dialects, some of them are so different from Mandarin they might as well be foreign languages. These are the Mandarin numbers in pinyin.
1. yi
2. er
3. san
4. si
5. wu
6. liu
7. qi
8. ba
9. jiu
10. shi
0.   -   ling
100.   -   bai
1000.   -   qian
10000.   -   wan
100000000.   -   yi (not to be confused with the number 1, this yi is tone 4, which means it is spoken with an accent at the beginning, like a quick muttering "yi!", while 1 is "yi....", dragged out slowly)

Unlike English, which uses multiples of one thousand for larger numbers, Chinese goes up to ten thousand, causing immense irritation because the irregularities in the two number systems. Similar to the English system, these units are stacked. yi wan is ten thousand, shi wan is a hundred thousand (ten times wan), and so on. er bai is two hundred, san bai is three hundred.

For mixed numbers (so to speak), one just adds characters by order of magnitutde. er bai wu shi is 250, er bai wu shi yi is 251. If there are zeroes in between, you add a ling to denote that there are no numbers in that multiple of 10. For example, wu bai ling yi would be 501, jiu wan ling shi would be 90010. Simple, no?

For ordinals, add a di in front of it.

The system has been standardized for eons, it is very simple and quite hard to make a mistake. Indeed, when I count I still do it the way I was taught as a child, using Cantonese, as Chinese numbers are definitely much more simple than English. The Cantonese numbers are quite different from the Mandarin ones.....

1. yut
2. yi
3. sam
4. se
5. mmm (yep, thats mmmm)
6. lok
7. tze
8. bat
9. gou
10. sap
See what I mean? Cantonese is probably the devil's dialect of Chinese, very few foreigners learn it properly.