How to quickly know the dimensions of an image?

Get Info

You can get the resolution from Get Info menu. Select the image and press ⌘ CMD+i, or right click on that image and choose Get Info menu item.

Image from cultofmac.com

QuickLook plugin

If you weren't on 10.9 - this lightweight QuickLook plugin called qlImageSize which can be found on GitHub lets You check the image size on the quicklook window title. I don't have any that work on 10.9, but perhaps this will help you if you wish to search for a similar one or report 10.9 compatibility to that project for improvement.

The fastest way is to have the resolution details visible all time ;)

Check out the step below:

*COLUMN VIEW

The simplest way from the command line is to use the built-in file command:

file ping-pong.png

Outputs:

ping-pong.png: PNG image data, 380 x 343, 8-bit/color RGBA, non-interlaced

More metadata will be displayed if available.

This will also work on Linux systems. See: https://superuser.com/questions/275502/how-to-get-information-about-an-image-picture-from-the-linux-command-line