Powering LED Lamp from Arduino
Number one, there is no way that Arduino will be able to supply power for an 120v AC light bulb. If you know that you are better off than some already!
I frequently point new Arduino users toward Arduino Playground, it has quite a bit of useful and important information about the basics.
If you want to make a 'lamp', you should investigate the links about connecting hardware to Arduino. AND…definitely learn &amp; understand the limits, capabilities, and limits of your Arduino. The following is very important and applies to almost every Arduino alive. Not knowing this may drastically shorten the life expectancy of your Arduino -

Absolute Maximum Ratings
DC Current per I/O Pin ........... 40.0 mA
DC Current VCC and GND Pins...... 200.0 mA
1 VCC pin: Means these Arduinos can Source a total of 200mA
2 GND pins: Means these Arduinos can Sink a total of 400mA

There are not only maximum current limits per pin and per board, there are also limits on total current per port (group of pins) too!
This Page has all the info you should need about that.
You will need to discover how much power (volts &amp; milliAmps) your 'lamp' will require. Then, you can determine how to power &amp; switch it properly. Anything I would consider a 'lamp' would likely need to be powered separately from Arduino and not through any of its pins or headers (common GND though!) and only switched on &amp; off using Arduino pins.