Here's my Subaru no-blower adventure.
Only the top speed worked and so I figured the blower motor resistor network is melted. Sure enough.
So for the dealer price of $62 I put in a new resistor which lasted all of one day.
Evidently the blower motor draws too much current.
I've never had a car like this.
So now I only have the top speed and I am making a much hardier one ohm high wattage resistor from left-over electric dryer heating element Nichrome wire, to give me half speed. Restoring the other speeds is not worth it to me at the moment.
Check for a blown fuse.
If the new fuse blows, post all the particulars for your car and I'll see if I can pull up a schematic.
If no fuse is blown you are looking for an open circuit and that is way easier than fighting with a short circuit but a schematic is usually necessary.
The thing is, almost any high school or college electrical geek can troubleshoot this simple series circuit of battery, fuse, switch and motor.
The problem is getting access to the wiring within the car, doping out the wire colors, penetrating the wire insulation (because connections can also fail and so they should also be treated as components).
If all these wires and components were laid out a table the fault could be found in five minutes. You check the current and measure voltages.