Debian Stable provides a newer kernel in backports. Here is how to install the newer kernel from wheezy-backports!
1. First add the following line to your /etc/apt/sources.list:
deb http://ftp.debian.org/debian/ wheezy-backports main non-free contrib
(Add this in addition to any other entries you may have in that file.)
$ sudo apt-get update
3. And finally here is an example for installing the backports kernel for a 64bit system:
$ sudo apt-get -t wheezy-backports install linux-image-amd64
Note that you may also need to install firmware from backports if using a laptop. For instance, my intel wifi needs this:
$ sudo apt-get -t wheezy-backports install firmware-iwlwifi
4. When all set, reboot and you are in with your new kernel.
$ sudo reboot
$ uname -a Linux bruckner 3.10-0.bpo.3-amd64 #1 SMP Debian 3.10.11-1~bpo70+1 (2013-09-24) x86_64 GNU/Linux