Nothing specific, but here's some general electric troubleshooting tips that apply.
Troubleshooting electrics requires methodic testing so you dont end up pulling your hair out. Confirm what you think you know and test what you don't, and move in methodic steps. required tool is a multimeter and set it to measure Voltage.
I'm assuming this circuit is made up of battery, fuse box/relay, resistor pack to give you speeds, amd switch. There might be more to it than that and a schematic diagram will help.
There is basically a circuit for the power to the blower, and a "subcircuit" to switch the relay. Two individual circuits that need to work together.
Step one is to plunge in the middle of the circuit to tell you which way to go. Pull the blower relay. The socket will have 4 terminals. One pair for switched power to blower, and one for the switch power. While the switch is on, you should have power across both pairs of connectors. If not, you either have a fault in the swicthing circuit or the blower power circuit.
Basically, if yes, then move a step closer in the circuit towards the blower; if ''no' move a step backward in the circuit to the source (battery).,
So you get all the way to the blower with 12V but the thing doesn't work, the blower motor is shot. if you trace the switch circuit all the way back and get 12 V tehn the switch is shot. Does this make sense?
Also, you can confirm anything you know by jumping power from the battery directly where you are.
Say you have determined there is 12V at the relay for the blower but not across the switch circuit. You could jump the relay with leads driect from teh battery and you would narrow it down to the swicth circuit. go slow and don't skip any steps if you arte organized you will track down the problem.