How do I modify a small blower motor to be variable speed?
For an electric motor to function, it has to alternate the voltage applied to its coils twice in each turn, so the electromagnetic force can produce a torque in the right direction always, given that half the time the magnet is behind the coil (and needs to be pulled), half the time ahead (and needs to be pushed).

There are two ways to do that alternation. For DC motors, you have to put some mechanism to do it; usually there's a set of brushes that touch the rotor to make electric contact, and the rotation itself makes the inversion happen (and there are brushless motors that use an electronic circuit to do the same thing). For AC motors, since the power source is itself alternating, you can rely on it to do that, and that's probably your case.

A dimmer with a variable resistor won't solve your problem because it'll reduce the output voltage, but not the AC frequency, the standard 60 Hz (50 Hz in Europe) the power grid provides, and the motor rotation is necessarily proportional to that frequency.

A more modern dimmer will cut the power periodically for a fraction of the time, using the same base frequency (thus 60 times a second). The more you turn its knob, the least the proportion of power mantained (and the least average voltage provided). But you still have 60 Hz, no matter what, and so your motor still won't be throttled down.

To control the speed of an AC motor you'll need something that can change the voltage AND the frequency provided to it, and that's a much more complex circuit.

What your friend mentioned is valid but is not the entire solution. It is true that you have a dimmer more powerful than you need; its maximum current needs to be higher than it's required by the motor (and with a good safety margin), but if it is, it doesn't matter if it's 50% higher or 200% higher. So a 15A dimmer has too much, unneeded current capacity. 
Nonetheless, it'll perform exactly as the one you have, and won't work either.