Electric cooling fan wiring question

Ok, so there is already a relay and you have two choices.
Connect the yellow to a switched power supply, or a non switched power supply.

Switched the fan will only be able to come on while the ignition is on, and non switched the fan will come on ang go off determined by the sensor.
(Even if the car is off)

You can connect the yellow wire to an accesory wire at the fuse box that only has power when the key is on for switched.
Or you can connect it directly to the battery positive at the battery or the relay and it will come on and go off as needed without the car running.

I prefer direct to the battery positive because it keeps the pressure down in the cooling system when the car is shut off causing the engine temps to climb.

If you use a test light or volt meter you can determin what accesory fuses are powered with the key on, then pull the fuse box down and splice into the wire, or use an accesory connector for fuse blocks.
You should also pull the fuse out and see which end of the fuse socket does not have power to it and connect at that side. (so the relay is on the fuse protected side)
Personally, I splice into the wire and solder, then heatshrink the joint.
(of course you have to put the heatshrink on the relay wire before you solder them.

The heatshrink can go onto your yellow wire and then bend the original wire at a 180 like this picture. (I showed it in red but but the heatshrink is on your yellow wire.
Once the soldering or whatever is done then slide the heatshrink down over the joint and heat it to shrink.

I hope this answered what you wanted to know.