How do you hook up one light to one switch in a basement lighting system that has all 10 lights connected to one switch?

If you have good access to the wiring this is relatively easy to do. Each of the 10 lights is connected to another in parallel in a "daisy chain" fashion. Light 1 is connected to the switch, light 2 is connected to light 1, light 3 is connected to light 2 and so forth.

Let's say it is light 5 that you wish to switch separately. You can first install the new switch by either adding a new box or modifying old switch box. There are two gang switches that will fit the form factor of a single switch.

TURN OFF THE POWER TO SWITCH BOX. Using the same supply input at original switch, add a new black wire to the wire nut for input to original switch and connect this to the input of new switch. Then run a new wire to light 5 and connect black wire to the output of new switch. Connect all the white wires together in switch box and separately connect all bare wires together in switch box.

Now at light 5 undo the black and white wire coming from the fixture, and reconnect the wire nuts so that there is a direct connection between light 4 and light 6. Do the same for the ground if present (bare wire). You now have the fixture wires hanging free. Now connect the black wire from new switch to the fixture black wire and white to white and you are done.