Your mac comes with it many language input sources other than English. To access them go to System Preferences. On the top row under personal the third icon from the right is Language and Text. Select that. Inside of language and text the far right tab is Input Sources; select that.
Scroll to where you see Simplified or Traditional Characters (depending on which you want). Then select which the specific input method you want, i.e. Pinyin, Wubi Xing, Wubi Hua.
Make sure that the “Show Input menu in menu bar” icon is selected.
To start writing go to the menu bar in the top right of the screen. It should currently have an American flag, if you are writing in American English. Click the that drop down bar and select the Chinese input method. Then go to wherever you want to type.
Pinyin (what most english speakers who learn Chinese use)
Start typing the pinyin. A white bar with suggestions of characters. To select the first option it suggests press the space bar. To use the other suggestions press the number that corresponds to the character you want. If you want to write english letters that you typed press the return key.