Outside light fixture
Im not going to say wether it is or is not correct to splice into an outlet to power your new ligh, but if you decide to do it, you would add a 14-2 romex to the box where the receptacle is, tying black to black/ white to white/ and copper to ground. Run the other end of that new romex into a single gang cut in box that you would add as close to the patio door as possible. Then run a 2nd new romex from that new box to the new light fixture tying same colors to each other again and ground to ground. Now go back to the new box and tie the two white wires together and put a wire nut on them. Then, take the black wire of the new romex coming from the receptacle and plug it into the bottom push-in or screw of a new switch. Then, take the black wire from the new romex going up to the light, and plug it into the top push-in or screw of the new switch. Tie the two ground wires from the romexes AND a 6" piece of extra bare copper wire together and put a wire nut on them. now take the loose end of the extra bare copper wire and connect it to the green ground screw on the new switch. Then neatly tuck all this into the new box and screw the switch into the box and put a new cover plate on it. Turn the power back on, put a light bulb in the new fixture and see what happens. With a little luck, the light should come on when you flip the switch to the up position. Good luck and first check with a real electrician to make sure the circuit can handle the new light.