Where to begin? (making lamp colour change when tapped)

I saw a lamp on a website and would love to have something like it for my mother. It’s far too expensive for me, though. So I thought I’d make one. It changes colour every time you tap it. The thing I’m unsure about, though, is what makes it change. How does this work and how can I start building something like it ASAP? Thank you for reading.

Lamp: http://www.firebox.com/product/7395/Mag … a=whatsnew

An accelerometer to detect the taps, some RGB LEDs, and a microcontroller would be reasonable building blocks.