Shut off the breaker that the furnace is hooked up to. Just turning the thermostat off is not sufficient. The furnace should not be receiving any electricity while you work on the repair.
Mark each wire going into the blower motor with colored tape so you remember where each wire goes. Unplug each wire from the blower motor once you're finished.
Unbolt the blower assembly from the furnace with a wrench by undoing the two or three bolts at the front of the assembly that hold it into the furnace housing.
Remove the motor from the blower if you just need to replace the motor. Unscrew the fitting by the motor wheel with a screwdriver and then undo the mounting bolts with a wrench. Pull the motor off.
Screw a new motor into the base of the blower by reattaching the screw and bolts you'd just taken off.
Slide the blower back into its housing in the furnace and bolt it back in place with the wrench.
Reattach the wires to the new blower in the same fashion as they were before.
Turn the breaker back on to restore power to the furnace and test it to make sure the blower works properly.