New shade, paint, or add embellishments.
When you say refurbish do you mean the looks or isn't it working? New look is like Kathy said - new shade, paint or add embellishments. If it isn't working it could be your power cord or the socket. Either can be purchased from Lowes, Home Depot or even Walmart. Start by pulling the socket from its bottom section and see if the wires from the power cord are still connected as that may be why it isn't working. If they are connected loosen the screws that attach the wires to the socket and remove the wires. Remove the bottom covering from your lamp carefully so you can reuse it. Then you can then carefully pull the cord from the lamp and replace it with a new one by feeding the new cord up through the lamp through the socket base and reconnect the socket. If you aren't sure about the socket you can replace that with a new one at the same time. After putting the wires on the socket push the socket back down into the base and carefully pull the cord straight in the lamp. You can check your lamp for operation then and if it works properly reattach the cover on the base of the lamp. Sounds complicated but it really isn't. I'm sure there are sites on the internet (You Tube) that can show you videos.
There are many ways to do that. I have used spray paint and contact paper both to refurbished the table lamps. Here is the tutorial I use to refurbished my lamps. Let me know if you need any other help please.
Ditto, have fun. Spray paint does wonders
You can paint it and get a new shade if all you want to do is make it look different. If you need to rewire or make any changes like that, then Darlene's advice above is the best course of action.