Go to the Control Panel and open Regional and Language Options.

Select the Languages tab and click Details. Also, make sure you’ve already installed the East Asian language files by checking the box below Details.

Click Add… and then select Chinese (Taiwan) for the input language. Microsoft New Phonetic IME 2002a should be selected by default under keyboard layout.

After clicking OK, make sure Microsoft New Phonetic IME 2002a is highlighted, then click on Properties… and choose the Keyboard Mapping tab. From that list, make sure HanYu Pinyin is selected, and click OK all the way back to the Control Panel.

Go to System -> Administration -> Language Support.

Scroll down the list and select Chinese. Then check the boxes for Input methods, Additional Fonts, and whatever else you find relevant. Also make sure that you’ve enabled support to enter complex characters by checking the box under Input method.

Right-click on the keyboard icon that should have appeared in the top right, near your clock (assuming you haven’t changed your configuration), and select SCIM Setup.

Select Global Setup under IMEngine, then check 智能拼音 under Chinese (simplified).

Left-click on the keyboard icon and choose the Chinese (simplified) input.

On the SCIM toolbar that appears, change 中 to 繁 to switch from simplified to traditional input. Note that there have been comments on how traditional Chinese input in Ubuntu isn’t very smart, with inputs sometime resulting in nonsensical phrases, so be wary of this.