Some years ago, Arduino was manufacturing this table lamp kit. The kit is now out of production, but here's the tutorial to build it from scratch.
Kit instruction manual cover
You can choose to control the lamp in multiple ways, my software and hardware implementation allows you to switch on the lamp trough hand gesture, change the brightness with a potentiometer, and change the LED colors using a simple button.
First of all, you need to assemble the lamp structure. The plexiglass is 3mm thick.
Build the circuit. You could start with a simpler version with a switch only, then add other components later. Be sure to find the right position in the breadboard for the components that needs to be inserted in the base holes. Customize colors and behavior.
Upload the code on the Uno and start playing with your lamp!