It's probably a very simple question, but I couldn't find the key to show the frame rate in KSP.
Assuming you're playing KSP on Steam, you can now use Steam's new FPS counter. Thanks to Steam's cross-platform nature, this should allow you to see your FPS on Linux and OSX as well.
You could always download the trial version of FRAPS to see your FPS.
The trial version only limits which features can be used, none of which are relevant to FPS monitoring.
If you happen to own a license for AIDA64 as well as any Logitech product with built-in LCD screen, such as the G19 or G510 Keyboard, or the G13 Advanced Gameboard, then you can monitor your FPS through AIDA64's Logitech LCD app (needs to be configured and activated first).
However, the FPS monitoring features of that app require FRAPS to be installed, even if it's just the trial version.
FRAPS currently supports Windows XP, Vista, 7 and 8 and will work with DirectX or OpenGL applications.