This short walkthrough describes how to install the Ubuntu linux kernel version 3.13  on without having to compile it yourself.

This guide should work with the latest version of Ubuntu Linux and most Ubuntu-based distributions including Mint. The included kernel files have been compiled using the generic Ubuntu configuration.

Installation Guide (GUI)

1. Download the kernel headers package:
   
   linux-headers-3.13.0-031300_3.13.0-031300.201401192235_all.deb
2. And the appropriate package for your system
   • AMD64: linux-headers-3.13.0-031300-generic_3.13.0-031300.201401192235_amd64.deb
   • I386: linux-headers-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb
3. And the accompanying compiled kernel image
   • AMD64: linux-image-3.13.0-031300-generic_3.13.0-031300.201401192235_amd64.deb
   • I386: linux-image-3.13.0-031300-generic_3.13.0-031300.201401192235_i386.deb
4. Install the files in the same order as downloaded above. So first install the headers and finally the image.
5. In the terminal run:
   
   sudo update-grub
6. Reboot and select the kernel from the bootloader menu

I will post the latest version of the 3.13 branch and 3.14-rc`s in comments below.