How do I Install a Windows Media Player MP4 Codec?

Microsoft provides what is known as the Codec Installation Package. This package includes the MP4 codec for Windows Media Player along with a lot of other commonly used codec.

Obtaining the Official Codec Package from Microsoft

First, go to www.microsoft.com, Downloads & Trials, and then the Download Center.
Once there, click Windows Media at the left panel. This will take you to a full download database of all files related to Windows Media.
On the Windows Media page, above, there should be a search box with "Windows Media" selected as the category. Input "codec" into the search field.
This will open up approximately 17 results. The one you want is called, "Codec Installation Package for Windows Media Player 7.1 or later." This codec package will support the current Windows Media Player 10 and 11.
Note that a validation as a customer running a genuine version of Microsoft Windows is necessary.
Validate, and the files should be ready for download.
Once the .exe file is downloaded, double click it to run it.
Users who are unfamiliar with the settings are highly recommended to just click "Next" and get the basic setup installed.

Using the K-Lite Mega Codec Pack

Note that the K-Lite Mega Codec Pack is not an official release from Microsoft. However, it is a highly supported and a very frequently updated pack. In fact, a recent survey on a technology site showed just as many users using this pack as there were for the official Microsoft's pack.

Go to http://www.free-codecs.com
At the left hand bar, there is a category called "Codec Packs"
Choose either the K-Lite Codec Pack or the K-Lite Mega Codec Pack, as they both will do the job.
Click the big "Download the K-Lite Mega Codec Pack."
The website will give you access to a page with a lot of download links spread across multiple mirrors. Whichever server you download from, the files will be the same.
Once the download is finished, run the .exe file by double clicking on it.
For non-experts, it is highly recommended to just install the recommended setup by clicking "Next."