how to use Nano instead of Uno3 to operate DC motors
It's my understanding that the Uno 3, Nano and Micro are the same in its basic form

Not exactly. The Uno and Nano use the same chip (the Atmega328p) and have the same pins broken out. The Arduino Pro Mini also uses that chip, but I think the pinout is a bit different. But mostly a code can be reused between these boards. The Arduino Micro uses an ATmega32U4, which is a different chip. Depending on the actual code, you might not be able to just reuse the code. Then you might have to change to code to use the Micros hardware.

with the motors as small as they are is it really necessary to have a motor shield or H bridges?

I would say yes. A digital output pin of an Arduino can only supply 20mA of current over longer time (absolute maximum 40mA). Even very small motors can easily exceed that. As long as you don't know the exact needed current in worst case (like stalling the motor), you should assume, that it is more than 20mA. Also a running motor generates a lot of electrical noise and the coils can induce backcurrents, that might destroy the output hardware of the Arduino pin (for that you need a flyback diode). And lastly, if you want to change the direction of the motor, you absolutely need an H-bridge. Otherwise it is only on or off.

Question is how do I wire up the Nano to do this

With H-bridges you normally need 3 pins to control the motor:

The enable pin (often marked as EN) enables or disables the motor (run or stop). You normally use analogWrite(en_pin, speed) to control the speed of the motor. It will send a PWM signal with the given duty cycle to the enable pin.
And you have 2 input pins (often marked as IN). They give you control over the direction.

IN1 to HIGH and IN2 to LOW will give you the first direction. Reversing to IN1 LOW and IN2 HIGH will give you the other direction. This will cause the H-bridge to lead the current through the motor in different directions.
Setting them to the same value will cause the motor to break (because that will short circuit the motors coil).



So you would wire 3 output pins of the Arduino to the mentioned pins on the H-bridge. It is up to you, what you want to use here. You can use a shield (which is normally the size of the Uno), you can use other ready to use motor driver boards (there are many) or you could build your own driver with a H-bridge chip and flyback diode.