Assuming you are in the US (so you have US-style electrical outlets) I found this:
I have never used one, and unfortunately it's out of stock, but it illustrates what you need to do what you want. You can make one yourself from parts, but if you are new to the game you might want something like this which is mostly complete.
As you can see, the power cord has a plug at one end and a socket at the other. You would disconnect your lamp from the wall outlet and plug this thing in instead, then plug the lamp into the other end. The plastic blob in the middle contains a solid-state relay, which breaks the supply wire from one end to the other. On the edge of the relay are some screw terminals. You need to connect one terminal to GND on the Pi, and another to a GPIO line on the Pi (so you need some wires that you can plug on to the GPIO header). Then you can use software on the Pi to turn the GPIO on and off, which will turn the relay on and off, which will turn the light on and off.
Since it's out of stock you can make one yourself by buying a solid state relay and cutting a power extension cord in half and rewiring it, but you must have confidence to do this, and you must have experience in making safe connections to mains-operated equipment. Maybe you could email adafruit and ask when it will be restocked, or try and find another supplier.