Using an Existing Power Source in the Ceiling
I had a chandelier in my dining room:
So I just removed it and used the existing wiring to power the recessed lights:
For my kitchen, I just used the wiring from the fluorescent light fixture I removed:
Running Wires from a Switch Controlled Power Outlet through the Wall
Since I didn't have an existing power source to the ceiling in my living room, I tapped in to a switch controlled power outlet and ran the wire up to the ceiling through the wall.
The red wire is the power from the switch so connect it to the black wire that will be run to the ceiling.
To get the wire from within the wall up to the ceiling, I just cut a notch in the drywall where the wall joins the ceiling: