Realtek RTL8101E

Kernel
Obviously you need to deactivate the r8169 driver. Either remove it completely:

and recompile, or if it's a module you can add it to the blacklist.

Edit:

You can also remove it with the command:

Note: If the built-in driver cannot removed by rmmod, please edit /etc/modprobe.conf and comment 'alias eth0 r8169'. Then, remove it again or reboot your computer. (See README from the Realtek driver for the configuration)

Install
Download the lastest version of the driver from this page

Uncompress

Compile

And install

It will be automaticaly loaded next time you boot, if you want to use it right away, just do :

For Kernel > 3.2
The drivers at the Realtek website are only for 2.6 and 2.4 kernels. If 8169 drivers are not compiled into the kernel, you can give that a try, and reboot.

Edit: The RealTek website now lists those drivers as suitable for kernel 3.x also. The latest version 1.023 does compile against kernel 3.3.8 but I've not tested it because on both my Intel DG945GCLF and my Intel D425KT the built-in r8169 driver now works (which it never did on 2.6).