Yes, a circuit(wire) that has 12volts when key is on, and 0volts when key is off, or in Accessory position.
You will need a test light or a Volt meter.
If you want to run the fog lights off the DLR relay then easiest way would be to get to either of the head light 12volt wires and tap that wire for the relay's coil.
A relay's coil doesn't draw any amps(under .5), which is why you use them, they can be added to a circuit without blowing fuses.
Relays have 4 connections(5 really), 2 are for the coil they have no + or - sides, when one coil connector is a ground and the other 12volts the coil turns into a magnet and pulls a metal bar down, this connects the other 2 connections on the relay, the Load.
The Load in this case would be the fog light switch(which is probably hooked to a relay as well, lol).
Fog light switch should have 2 wires connected to it, you can cut either one, but leave enough wire to splice longer wires on.
Headlight wire(or key on wire) is not cut, just bare a part of the wire and add your wire, or use trailer light crimp on taps.
Head light 12volt wire-------------your relays coil----------Ground
Fog light switch wire-------------your relays Load---------Fog light switch wire
When head lights come on relays coil gets power and closes Load connections
If Fog light switch is left on, fog lights will come on when relay closes, and go off when head light are off.
Automotive relays are cheap, should be under $10 for relay and socket
These relays have a standard numbering for connections, seen here: http://www.reuk.co.uk/Automotive-Relays.htm
85 and 86 are the coil
30 and 87 are the Load
87a is that 5th connection, doesn't matter if you get one with this or without this