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The Sino-Japanese system uses kanji characters to represent each number. The pronunciations of these characters differ from the pronunciations of the native Japanese characters. Use flashcards or a similar system to memorize these characters and their pronunciations.  One (1) is 一 (ichi, pronounced "ee-chee"). Two (2) is 二 (ni, pronounced "nee"). Three (3) is 三 (san, pronounced "sahn"). Four (4) is 四 (shi, pronounced "shee"). Because this word sounds like the Japanese word for death, the alternate pronunciation yon is also used – especially when talking about people. Five (5) is 五 (go, pronounced "goh"). Once you've memorized the kanji characters and pronunciations of the numbers from 1 to 5, add the next 5. Practice until they come as smoothly as the first five. Then you are able to count to 10 using the Sino-Japanese system.  Six (6) is 六 (roku, pronounced "loh-koo"). Seven (7) is 七 (shichi, pronounced "shee-chee"). Because this has the same shi sound as in the number four, the alternate pronunciation nana is common. Eight (8) is 八 (hachi, pronounced "hah-chee"). Nine (9) is 九 (kyuu, pronounced "kyoo"). Ten (10) is 十 (juu, pronounced "joo"). Once you know how to count to 10, creating larger numbers is a breeze. Unlike in English and other European languages, there are no new words to learn. If you break the number down into its parts and combine the symbols for each of those parts, you can count all the way to 99 with 10 characters. For example, 31 is 三十一: three tens and a one. You say it san juu ichi. 54 is 五十四: five tens and a four. You say it go juu shi. If you want to refer to the "first" or "second" rather than the cardinal number, put a 目 after the number. Then read the number and the 目 together.  For example, 一 目 means "first." You would read it ichi me (pronounced "ee-chee meh"). You do the same thing with larger numbers. For example, 三十一 目 means "thirty-first." However, in most cases you would be talking about the 31st something, such as the 31st time or someone's 31st birthday. To say that, you would need an additional character, known as a counter, that is appropriate for that thing.
Memorize the symbols and words for the numbers from 1 to 5. Move on to the symbols and words for the numbers from 6 to 10. Combine symbols to create larger numbers. Add 目 (me, pronounced "meh") to use a number as an ordinal.