An AOSP build of Android 4.4 KitKat for the Nexus 4 has been finalized by the folks at Paranoid Android, and is available for download. A similar build is available for the Nexus 7.
Google has mentioned that devices like the Nexus 4 and Nexus 7 will get the official Android 4.4 KitKat update in the coming weeks. For those unwilling to wait, Paranoid Android has posted an Android 4.4 build that is based on the AOSP codebase.
You can download the ROM from here, and then flash it on your device. Considering this is the first build to come out, it will be buggy, and is said to crash the Calendar and Search utilities. Also note that flashing this ROM will delete all data that is stored on the device, and for now the ROM can only be flashed by using the ClockworkMod tool.