Let's assume, that you have several graphic cards on your desktop, and you want to see more details about them, because you dont remember exact model number and other stuff.
My first look is always lspci but it wont give you the full view.
Before using lspci, it's a good idea to update PCI ID list with the latest version

deadfish ~ # update-pciids
Downloaded daily snapshot dated 2014-05-02 03:15:01


deadfish ~ # lspci |grep VGA
00:02.0 VGA compatible controller: Intel Corporation Device 0402 (rev 06)
03:00.0 VGA compatible controller: ATI Technologies Inc Device 67b1
04:00.0 VGA compatible controller: ATI Technologies Inc Device 67b1
05:00.0 VGA compatible controller: ATI Technologies Inc Device 67b1
06:00.0 VGA compatible controller: ATI Technologies Inc Device 67b1
deadfish ~ # 


deadfish ~ # lspci -v -s 06:00.0
06:00.0 VGA compatible controller: ATI Technologies Inc Device 67b1 (prog-if 00 [VGA controller])
        Subsystem: PC Partner Limited Device e285
        Flags: bus master, fast devsel, latency 0, IRQ 19
        Memory at 80000000 (64-bit, prefetchable) [size=256M]
        Memory at 90000000 (64-bit, prefetchable) [size=8M]
        I/O ports at a000 [size=256]
        Memory at f7800000 (32-bit, non-prefetchable) [size=256K]
        Expansion ROM at f7840000 [disabled] [size=128K]
        Capabilities: [48] Vendor Specific Information: Len=08 <?>
        Capabilities: [50] Power Management version 3
        Capabilities: [58] Express Legacy Endpoint, MSI 00
        Capabilities: [a0] MSI: Enable- Count=1/1 Maskable- 64bit+
        Capabilities: [100] Vendor Specific Information: ID=0001 Rev=1 Len=010 <?>
        Capabilities: [150] Advanced Error Reporting
        Capabilities: [200] #15
        Capabilities: [270] #19
        Capabilities: [2b0] Address Translation Service (ATS)
        Capabilities: [2c0] #13
        Capabilities: [2d0] #1b
        Kernel driver in use: fglrx_pci

deadfish ~ #

Another metchod to detect a video card is lshw

deadfish ~ # lshw -short -c video
H/W path         Device     Class          Description
======================================================
/2/100/2                    display        Xeon E3-1200 v3/4th Gen Core Processor Integrated Graphics Controller
/2/100/1c.4/0               display        Hawaii PRO [Radeon R9 290]
/2/100/1c.5/0               display        Hawaii PRO [Radeon R9 290]
/2/100/1c.6/0               display        Hawaii PRO [Radeon R9 290]
/2/100/1c.7/0               display        Hawaii PRO [Radeon R9 290]

When you need even more details about your card, you have to use some tools that comes with drivers.

For ATI it will be aticonfig or atitweak and for NVIDIA you will use nvidia-smi