The technical name of my Ethernet Card is "Atheros AR8151 PCI-E Gigabit Ethernet Controller (NDIS 6.20)".
Installing Debian with my CD
I found that when I installed Debian and I followed the steps below, I could start using the Internet:
To begin with, I connected my computer to the Internet directly.
I selected "advanced options" and "automated install".
See the related article here.