will give u over idea about wht u r looking for...
in the bottom of the output u will find wht driver u have.... Ex:06:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E PCI Express Fast Ethernet controller (rev 01)
its very simple the way is you need to download RTL8101E from realtek web-site here is the link here
go to extracted folder
#make clean modules
#insmod ./src/r8101.ko (or r8101.o for kernel 2.4.x)
after rebooting the system your system able to connect to internet through LAN,if not type this command in terminal
#/sbin/services network restart