How can I find out if my Ethernet card (NIC) is being recognized or not?

Ethernet card is lifeline of any Linux server. So if you need to find out find out if your Ethernet card is being recognized or not then use dmesg, ifconfig, or netstat command. Command ifconfig can be use to configure a network interface card as well as to find out information about Ethernet card. If you want find out NIC Ethernet chip set then you can use lspci command (see below for an example of lspci).

# /sbin/ifconfig

Output:

eth0      Link encap:Ethernet  HWaddr 00:0F:EA:91:04:07
   inet addr:192.168.1.2  Bcast:192.168.1.255  Mask:255.255.255.0
   inet6 addr: fe80::20f:eaff:fe91:407/64 Scope:Link
   UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
   RX packets:64874 errors:0 dropped:0 overruns:0 frame:0
   TX packets:65189 errors:0 dropped:0 overruns:0 carrier:0
   collisions:0 txqueuelen:1000
   RX bytes:50448703 (48.1 MiB)  TX bytes:13648924 (13.0 MiB)
   Interrupt:18 Base address:0xc000

Note If you get output eth0 then your card is being recognized.
The dmesg program helps users to print out their bootup messages. Messages are stored in /var/log/dmesg (Debian Linux):
# cat /var/log/dmesg |grep -i eth0

Output:

eth0: RealTek RTL8139 at 0xc000, 00:0f:ea:91:04:07, IRQ 18
eth0:  Identified 8139 chip type 'RTL-8100B/8139D'
eth0: link up, 100Mbps, full-duplex, lpa 0x45E1

OR

# dmesg | grep -i eth0

Display a table of all network interfaces:
# netstat -i

Output:

Iface   MTU Met   RX-OK RX-ERR RX-DRP RX-OVR    TX-OK TX-ERR TX-DRP TX-OVR Flg
eth0   1500 0     64858      0      0      0    65172      0      0      0 BMRU
eth0:  1500 0       - no statistics available -                            BMRU
lo    16436 0      8133      0      0      0     8133      0      0      0 LRU

Find out NIC chipset
For further troubleshooting of your Ethernet card (NIC) I recommend to use lspci command. lspci is a utility for displaying information about all PCI buses in the system and all devices connected to them.
lspci | less
OR
lspci | grep Ethernet

Output:

0000:01:05.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL-8139/8139C/8139C+ (rev 10)

In above example I have "Realtek Semiconductor" NIC with RTL-8139/8139C/8139C chip set.