How Do You Install A String Of Lights From A Ceiling Fan Outlet?

You said you have a plug, the problem may be, is it a switched plug, or one that is hot all the time? If it is one that stays hot, you will need to get a professional in and install a wall switch. Or you will have to put a switch on the cord before any lights are connected.
Go to the electrical dept at one of the home omprovement stores, and you can buy the electrical cord and the sockets for the bulbs, like you see at church picnics. Good luck

Call Home Depot! You’ll probably need to purchase a very inexpensive thingy to install that is the “normal” thing you screw lights into. Be sure you get the kind that has 2 electrical plug ins, as well. Just tell them what you want to do and they will show you how to do it and give you the stuff (to buy). I love them, they really know how to do the stuff they sell.

Cut the plug off the wire on the lights. Separate the two strands and remove the insulation to expose about 1/2 inch of wire. Connect white to white, black to black, and if there, green to ground (may be completely exposed copper). Drill a small hole in the plate BEFORE you make the connections and slide the plate down the wire. Once the connections are made, secure the wire nuts with electrical tape. Test the lights. Slide the plate up to the box and screw back into place. Fasten lights to ceiling as planned.
Be sure to turn off the power BEFORE you start playing with the wiring.
If in doubt, have someone do it for you.