Make sure all the prerequisite KBs are installed first, especially KB2919442:
How to install Windows 8.1 Update manually or using Windows Update
Technical Level : Intermediate
Summary
Windows 8.1 Update continues Microsoft’s refinement of its current version of Windows, presenting even greater accessibility to functionality such as Power and Search once hidden in hot corners and menus. Other noticeable changes include title bars, minimize and close buttons now available in modern apps. Another great feature includes the ability to pin your favourite modern apps to the Windows Taskbar. Lets take a quick look at getting it up and running on a Windows 8.1 install.
Details
Please note, before you can install this update, you need to first ensure you Windows 8.1 installed. If you have Windows 8 which was launched in October 2012, this update will not apply to you. If you want to take advantage of the improvements offered in the Windows 8.1 Update, see instructions at the following link how to upgrade from Windows 8 to Windows 8.1:
http://techingiteasy.wordpress.com/2013/10/17/how-to-upgrade-from-windows-8-to-windows-8-1/
Backup:
Just as a precaution, you should backup your computer.
See the following How To Geek article about how to do so:
http://www.howtogeek.com/167984/how-to-create-and-restore-system-image-backups-on-windows-8.1/
Please note, this is standalone Windows Update installers I am using which requires installation in a specific order. On April 8th, Windows Update will take care of this, but for this article sake, I will describe the experience. Depended on your system, Windows 8.1 Update 1 is provided as 6 updates, in my case, I only needed to apply 5, since KB2919442 was already installed.

Recommended Install Order
1. KB2919442
2. KB2919355
3. KB2932046
4. KB2937592
5. KB2938439
6. KB2949621
Download links for Windows 8.1 Update x86:
KB2949621-v2 (Windows Server 2012 R2 only)
Download links for Windows 8.1 Update x64:
KB2949621-v2 (Windows Server 2012 R2 only)
Download links for Windows 8.1 Update ARM:

The biggest one of them all is KB2919355, which took quite a while to install. In fact, I did this on my work computer around 3:30 PM and I leave work at 4:30, KB2919355 took about 30 minutes be completed and required a reboot. I recommend you do this at a convenient time.