If you're interested in reading and writing Chinese characters, there's no better place to get started than with the numbers 1-10. They are quite simple to write, useful to know, and are exactly the same in both the traditional and simplified writing systems.
So grab a piece of paper and a pencil, give a click on the links below, and try to write the characters with proper stroke order as demonstrated:
| One | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | 
| 一 | 二 | 三 | 四 | 五 | 六 | 七 | 八 | 九 | 十 | 
Now that you know these characters, you actually know how to read and write all the numbers through 100. That's because Chinese follows a very simple pattern for counting:
| 11 | = | 10 + 1 | = | 十一 | 
| 12 | = | 10 + 2 | = | 十二 | 
| 20 | = | 2 + 10 | = | 二十 | 
| 21 | = | 2 + 10 + 1 | = | 二十一 | 
| 28 | = | 2 + 10 + 8 | = | 二十八 | 
| 82 | = | 8 + 10 + 2 | = | 八十二 | 
| 99 | = | 9 + 10 + 9 | = | 九十九 | 
Ready for a challenge? Let's try something a little more interesting:
| English: | Love | Beauty | Courage | Dragon | Fire | 
| Simplified: | 爱 | 美 | 勇气 | 龙 | 火 | 
| Traditional: | 愛 | same | 勇氣 | 龍 | same | 
Because the Chinese simplified system is based on the traditional one, many characters are exactly the same, as we saw with the the numbers 1-10. Even for characters that aren't the same, you will often be able to see similarities. For example, have a look at the character for "love" in the simplified and traditional systems. Almost the same, right?
To get a bit more practical, here are the 25 most frequently used characters in the Chinese language: 
Source: http://technology.chtsai.org/charfreq/
| (a  possessive particle)  |  is,  are, yes  |  not,  no  |  I,  me, my  |  one | have,  has  |  big | located,  at  |  person,  people  |  past  tense particle  |  middle | until,  arrive  |  |
| Simp | 的 | 是 | 不 | 我 | 一 | 有 | 大 | 在 | 人 | 了 | 中 | 到 | 
| Trad | same | same | same | same | same | same | same | same | same | same | same | same | 
| money,  supply  |  to  want, need  |  can | can | this | (common  measure word)  |  you | will,  meet  |  good | do  something for someone  |  up,  above, get on  |  to  come  |  |
| Simp | 资 | 要 | 以 | 可 | 這 | 个 | 你 | 会 | 好 | 为 | 上 | 来 | 
| Trad | 資 | same | same | same | same | 個 | same | 會 | same | 為 | same | 來 | 
Want to keep going?