I'm trying to wire up a Bosch style relay and a toggle switch to turn my radiator fan on and off when I want to, the toggle switch is obviously inside the vehicle. I found this diagram online but I'm still confused on what goes where, any help is appreciated!

Think I would do it differently. The Bosch style SPDT automotive relay should be rated for 30/40 Amps and have a 5 wire harness.
I would wire it up with the relay in the engine compartment near the battery and fan, pulling power right off the battery. I would
also control the relay with the switch inside the cab using the Accessory wire so the fan could only be on with the key in the
ignition at the ACC or RUN positions ( but off when cranking the starter ). Here is the wiring.
One side of toggle switch to ACC wire at ignition switch thru 3 Amp fuse. Should be a 12 Gauge Orange wire at the ignition switch harness. 18 Gauge wire
Other side of toggle switch to engine compartment and Relay Pin 86. 18 gauge wire
Relay Pin 85 to Chassis ground or Battery negative terminal. 18 gauge wire
Relay Pin 87 to Battery positive terminal thru 30 Amp fuse. 12 gauge wire
Relay Pin 30 to Fan (+) connection. 12 gauge wire
Relay Pin 87A not used ( insulate or remove )
Other side of fan to Chassis ground or Battery negative terminal. 12 gauge wire.
The relay should have the pins marked.
-------------
Soldering is fun!
Or this:-
fan.bmp
I'm using BMW colours 87a not used. In your original diagram the light goes out when the fan is switched on.
Also if this is a cooling fan, I'm a bit worried about current capacities, a 40 amp relay is borderline also 16 GA wire? Go to 12 GA.
Switch in car and run to wires through to engine bay, one for the relay + feed to the fan motor wire, relay 30; the other from the switch to relay 85.
-------------
Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.
Great, thanks for the replies they make perfect sense! Now next question, if I wanted to add a transmission cooler fan with toggle switch could I wire it to the radiator fan relay and power both fans or do I need a 2nd relay? I've got a SPST 4 wire relay and a toggle switch I could use if I can't power both fans on one relay.
Same circuit again, you need another relay, the current draw is too much. but both ideas are pretty useless against a thermal (A.K.A. "Otter" switch) acting as a temperature dependant switch bringing on the fan(s) automatically.
-------------
Amateurs assume, don't test and have problems; pros test first. I am not a free install service.
Read the installation manual, do a search here or online for your vehicle wiring before posting.