If the question is, can I wire a switch to an existing light fixture (and I must assume that it's something like a pull-chain light fixture), the answer is yes.
If the question is, "how do I wire a switch to an existing light fixture that has no external switch", the answer is, "in series".
The attached web site gives simple instructions on how to wire a basic light switch to an existing light.
See sources and related links below
Piggyback off the box for the existing light. Run a wire from the existing junction box to a new junction box (which is placed wherever you want the new fixture). Then, in the existing box, connect the wire coming from the switch, the wire for the existing fixture, and the wire for the new fixture together using wire nuts. Wire up the new fixture, and presto, you have two fixtures on a switch where there was only one before.
To control a light with a switch, the switch has to be connected in series with the light fixture.
The light is wired the same as any voltage fixture. Bring the source voltage to the fixture and connect it to the two fixture wires. If you want to control the off-on of the fixture take the source voltage to a switch first and then out of the switch to the light fixture.
Your question implies that you want to wire a new branch circuit controlled by a switch using the existing light fixture. DON'T DO IT! It is a code violation. The existing light has a switch already. you cannot control another light with another switch when the first light is OFF. There are safety reasons for not doing this. If you wire the new light from the hot side of the existing light, you can be shocked even if the new switch is OFF.
Connect the ground wire from the light fixture to the ground wire in the ceiling box.
If you are adding the pull chain to an existing fixture then the pull chain switch should have two wires. Wire nut either one to the hot wire coming in and the other to the black wire of the fixture.
It just holds the bulb, does not have a switch in the fixture.
Two options. Change the fixture to a keyed pull-chain, or add a pull-chain adapter to the existing fixture. Both available from Home Depot and others for about $3.
The fixture will not be grounded. As long as the hot and neutral are connected the light will work.
You have both a mechanical and electrical issue. From a mechanical standpoint you need the switch mounted securely in the fixture. The switch will have two black wires or two terminals. You need to insert the switch in series with the black wire going to the fixture. Let's say that the black wire from a supply is connected to the black wire in the fixture with a wirenut. Undo the two wires and connect each wire to a wire on the switch.
Install the switch in the wall outlet box you have installed. Now run a 12/2 or 14/2 wire from the switch to the light fixture in the ceiling. Run the exact same size wire that is already powering the light. Connect the ground wire coming from the light switch to the ground wires in the ceiling box. At the light in the ceiling cut the black wire powering the light. Cut only that wire. Now strip the 2 black wires back and connect the white wire coming from the wall switch to one of the black wires and the black wire coming from the wall switch to the other black wire. At the wall switch connect the ground wire to the ground screw on the single pole switch. Now connect the white and black wire to either screw. Does not matter which one. Now when you turn the switch off you are breaking the flow of electricity to the light. This is called a switch leg.