Input of Simplified Chinese on Windows
It depends on the OS you're in. On answers.microsoft.com I searched chinese and you can see the solutions for each OS from Microsoft.

Just for completeness, let me add also a quick guide for the Mac OS X. You do the following:


Go to System Preferences (you can reach it in the menu by clicking on the apple symbol on the top-left side);
Click on "Language and Text" or something similar, it has a flag icon;
Click on the "Input source" tab;
Scroll down until you see "Chinese - Simplified" or "Chinese - Traditional";
Select the input type you desire;
You can select the language input by clicking on the Flag on the top bar, near the time and the battery level.


Now open a document. If you selected the "pinyin input" type, which is the most used (sometimes the only one available) and the easiest one, then you can type the "alphabetical" version of the characters, which is called pinyin, indeed. 

For example, if you wanna write "你好", type "nihao". A menu will "open". To select one of the choices, click on the number that corresponds to the expression you wish to write and voilà. Below you'll see the menu I was talking about:



By clicking one, I choose to write the two characters that correspond to "nihao" which mean "hello". 

On the Mac it is also possible to draw using the trackpad or an external graphic tablet:



This was done like the video showed in the Apple support page.