What are the minimum system requirements to run Photoshop?

It depends which version are you installing and on which system either on Windows or MAC, each has different requirements.

CS6 on windows required 

Windows

• Intel® Pentium®4 or AMD Athlon®64 processor
• Microsoft® Windows® XP with Service Pack3 orMicrosoft Windows7 with Service Pack1. Adobe® Creative Suite®5.5 and CS6 applications also support Windows8 and Windows8.1. See the CS6 FAQ for more information about Windows8 support.*
• 1 GB of RAM
• 1 GB of available hard-disk space for installation; additional free space required during installation (cannot install on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with16-bit color and512 MB (1 GB recommended) of VRAM
• OpenGL2.0–capable system
• DVD-ROM drive
• This software doesn't operate without activation. Broadband Internet connection and registration are required for software activation, validation of subscriptions, and access to online services.† Phone activation is not available.

Windows

• Intel® Pentium®4 or AMD Athlon®64 processor (2 GHz or faster)
• Microsoft® Windows®7 with Service Pack1, Windows8, or Windows8.1 *
• 1 GB of RAM
• 2.5 GB of available hard-disk space for installation; additional free space required during installation (cannot install on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with OpenGL®2.0,16-bit color, and512 MB of VRAM (1 GB recommended)**
• Internet connection and registration are necessary for required software activation, membership validation, and access to online services.†

depends what you have to edit.

if you have to edit big file (professional printing ) then go for good mechine

with more than4 gb of RAM and al least intel i5

Which vershion of photoshop?and what platform?

Because now photoshop light can run from a mobile device (Android Or IOS) OR Adobe creative cloud vershion can run through updated  internet browser.

from Photoshop7.0 (Starter recommeded vershion) to CS6 will be install and use from different computing power. 

It depends on combination of: operating system / Photoshop version / size of the files we work with, hardware we have... I remember back in1999 configuration I worked on: Intel Celeron333mhz,64mb or SDRAM, VGA with8mb of video memory... it hardly managed high res files but it worked :) After all, I would invest in RAM. If we have enough RAM, we will avoid disk scratch that slows down PC rapidly...

Minimum system Requirements:

Adobe Photoshop CC.

Windows:

• Intel® Pentium®4 or AMD Athlon®64 processor (2 GHz or faster)
• Microsoft® Windows®7 with Service Pack1, Windows8, or Windows8.1 *
• 1 GB of RAM
• 2.5 GB of available hard-disk space for installation; additional free space required during installation (cannot install on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with OpenGL®2.0,16-bit color, and512 MB of VRAM (1 GB recommended)**
• Internet connection and registration are necessary for required software activation, membership validation, and access to online services.

Mac OS

• Multicore Intel processor with64-bit support
• Mac OS X v10.7, v10.8, or v10.9
• 1 GB of RAM
• 3.2 GB of available hard-disk space for installation; additional free space required during installation (cannot install on a volume that uses a case-sensitive file system or on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with OpenGL2.0,16-bit color, and512 MB of VRAM (1 GB recommended)**
• Internet connection and registration are necessary for required software activation, membership validation, and access to online services.

• Intel® Pentium®4 or AMD Athlon®64 processor

• Microsoft® Windows® XP with Service Pack3 orMicrosoft Windows7 with Service Pack1. Adobe® Creative Suite®5.5 and CS6 applications also support Windows8 and Windows8.1. See the CS6 FAQ for more information about Windows8 support.*
• 1 GB of RAM
• 1 GB of available hard-disk space for installation; additional free space required during installation (cannot install on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with16-bit color and512 MB (1 GB recommended) of VRAM
• OpenGL2.0–capable system
• DVD-ROM drive
• This software doesn't operate without activation. Broadband Internet connection and registration are required for software activation, validation of subscriptions, and access to online services.† Phone activation is not available.

Mac OS

• Multicore Intel processor with64-bit support
• Mac OS X v10.6.8 or v10.7. Adobe Creative Suite3,4,5, CS5.5, and CS6 applications support Mac OS X v10.8 or v10.9 when installed on Intel-based systems.**
• 1 GB of RAM
• 2 GB of available hard-disk space for installation; additional free space required during installation (cannot install on a volume that uses a case-sensitive file system or on removable flash storage devices)
• 1024 x768 display (1280 x800 recommended) with16-bit color and512 MB (1 GB recommended) of VRAM
• OpenGL2.0–capable system
• DVD-ROM drive
• This software doesn't operate without activation. Broadband Internet connection and registration are required for software activation, validation of subscriptions, and access to online services.† Phone activation is not available.

More: http://helpx.adobe.com/x-productkb/policy-pricing/system-requirements-photoshop.html

new version needs at least C2D for better performace otherwise low systes can do the job as well.