I am a new Linux system user. I am using Ubuntu Linux. I do not want to open up the computer hardware to just see the make and model of the graphics card in a system. How do I find out which graphics card installed in my Linux desktop system?

You do not have to open the hardware/desktop/laptop to see the make and model of the graphics card in a system. There is a direct method provided by using lspci and other commands on Linux to get hardware information. You need to use the following commands:

1. lspci command
2. lshw command
3. grep command
4. update-pciids command
5. GUI tools such as hardinfo and gnome-system-information command.

Download new version of the PCI ID list

First, grab the current version of the pci.ids file from the Internet:
$ sudo update-pciids
OR
# update-pciids
Sample outputs:

[sudo] password for nixcraft: 
Downloaded daily snapshot dated 2014-01-09 03:15:01

How to check graphics card on Linux

Type the following lspci command. It will usually tell you the vendor and model of your card. Open the Terminal/xterminal or shell prompt and type the command:
$ lspci
$ lspci -v
$ lspci -v | less

Sample outputs:

00:01.0 PCI bridge: Broadcom BCM5785 [HT1000] PCI/PCI-X Bridge
00:02.0 Host bridge: Broadcom BCM5785 [HT1000] Legacy South Bridge
00:02.1 IDE interface: Broadcom BCM5785 [HT1000] IDE
00:02.2 ISA bridge: Broadcom BCM5785 [HT1000] LPC
00:03.0 USB Controller: Broadcom BCM5785 [HT1000] USB (rev 01)
00:03.1 USB Controller: Broadcom BCM5785 [HT1000] USB (rev 01)
00:03.2 USB Controller: Broadcom BCM5785 [HT1000] USB (rev 01)
00:05.0 VGA compatible controller: ATI Technologies Inc Rage XL (rev 27)
00:18.0 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] HyperTransport Technology Configuration
00:18.1 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Address Map
00:18.2 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] DRAM Controller
00:18.3 Host bridge: Advanced Micro Devices [AMD] K8 [Athlon64/Opteron] Miscellaneous Control
01:0d.0 PCI bridge: Broadcom BCM5785 [HT1000] PCI/PCI-X Bridge (rev b2)
01:0e.0 RAID bus controller: Broadcom BCM5785 [HT1000] SATA (Native SATA Mode)
02:03.0 Ethernet controller: Broadcom Corporation NetXtreme BCM5704 Gigabit Ethernet (rev 10)
02:03.1 Ethernet controller: Broadcom Corporation NetXtreme BCM5704 Gigabit Ethernet (rev 10)

Look for video controller / vga / 3D keywords in above output listing. Please note that if you do not see your card, try updating pci database. It is a good idea to run update-pciids command to fetches the current version of the pci.ids file from the primary distribution site and installs it. You must run update-pciids command as root user:
$ sudo update-pciids
OR
# update-pciids

Example: Find out the model of my graphics card on my Laptop powered by Linux

Type the following command:
$ lspci | grep -i --color 'vga\|3d\|2d'
Sample outputs:

01:00.0 VGA compatible controller: NVIDIA Corporation GK104GLM [Quadro K5000M] (rev a1)

Please note the device ID # 01:00.0. Now, to get detailed information, enter:
$ sudo lspci -v -s 01:00.0
Sample outputs:

Hardware information GUI tool

Under Ubuntu or any other Linux distro, you can open hardware information GUI tool by clicking on:
System > Preferences > Hardware information
Sample outputs:

hardinfo – System Information GUI tool

You can install hardinfo with yum command or apt-get command:
$ sudo apt-get install hardinfo
Run it as follows:
$ hardinfo
Sample outputs:

lshw command

The lshw command provides detailed information on the hardware configuration of the machine. You can install it with yum or apt-get command:
# lshw -short
# lshw -short | grep -i --color display
Sample outputs:

/0/100/1/0                   display        GK104GLM [Quadro K5000M]

OR get detailed information:
# lshw -class display
Sample outputs:

  *-display               
       description: VGA compatible controller
       product: GK104GLM [Quadro K5000M]
       vendor: NVIDIA Corporation
       physical id: 0
       bus info: pci@0000:01:00.0
       version: a1
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress vga_controller bus_master cap_list rom
       configuration: driver=nvidia latency=0
       resources: irq:16 memory:f5000000-f5ffffff memory:e0000000-efffffff memory:f0000000-f1ffffff ioport:e000(size=128) memory:f6000000-f607ffff

A note about Nvidia GPU users with Nvidia binary drivers

Just type the following command to get detailed information about NVIDIA GPU card:
$ nvidia-smi
Sample outputs:

Mon Jan 13 04:08:34 2014       
+------------------------------------------------------+                       
| NVIDIA-SMI 5.319.32   Driver Version: 319.32         |                       
|-------------------------------+----------------------+----------------------+
| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |
| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |
|===============================+======================+======================|
|   0  Quadro K5000M       Off  | 0000:01:00.0      On |                  N/A |
| N/A   41C    P8    N/A /  N/A |       64MB /  4095MB |      0%      Default |
+-------------------------------+----------------------+----------------------+
                                                                               
+-----------------------------------------------------------------------------+
| Compute processes:                                               GPU Memory |
|  GPU       PID  Process name                                     Usage      |
|=============================================================================|
|  No running compute processes found                                         |
+-----------------------------------------------------------------------------+

Or GUI tool called nvidia-settings
$ nvidia-settings