Using numbers in Korean is very similar to Japanese and Chinese because those three use same Chinese numbers with different pronunciations. But this fact is applied for only cardinal numbers(one, two, three, ...), not ordinal numbers (eg. first, second, third, ...).

Basic Reading

Actually, these ordinal numbers are not actually ordinal. They are original-Korean numbers, and used to make real ordinal numbers in some contexts. (So if you use this forms as it is, it's not an ordinal number. To know how to use them, see the end of this post.)

English-like languages have special notations for 11 and 12, but Korean-like languages doesn't have such exceptions.

English puts a comma between every 3-digits because it uses 'thousands' scaling, but Korean puts it between every 4-digits because it uses 'ten-thousands(만)' scaling. However, 3-digits separation is more frequently used in the real life such as banks.

Some examples:

If you use 1 in places of larger than 10000, we usually add a prefix '일'(1) to the number. So 1000,0001 is 일억일, not 억일, but 1,0000 is 만, not 일만. (You may use '일만', but it's only in some formal notations.)
It's easy to think the last example as 1x10⁸ (일x억) + 2345x10⁴ (이천삼백사십오x만) + 6789x1 (육천칠백팔십구). If you want test yourself, there is a perl script that converts arabic numbers to Korean pronunciations. (Note that the script uses CP949 or EUC-KR encoding, not UTF-8. But I think if you copy & paste its source code in UTF-8 encoding, then it will run well in UTF-8 encoding.)

Floating numbers

To speak floating numbers, you can say '.' as 점, and the following digits in 1-digit numbers, such as:
10.13579 = 십점일삼오칠구
365.2422 = 삼백육십오점이사이이

For more mathematical notations such as equations, fractions and squares, I will introduce them (maybe far-_-) later.

Using ordinal numbers

If you use ordinal numbers as the attributive forms, the last sounds in 2, 3, 4 and 20 are dropped. The affix '-째' is something similar to '-th' in English.

and so on.

You can read an article about Korean numerals on Wikipedia instead of this.