Even if you don't use the motor shield itself, you can look at the circuit and the code for suggestions on what to do.
The simplest way to drive a DC motor is just to turn on the power. A half bridge controls power to the motor by creating low-resistance connections to the high or low voltage rails, depending on what you tell it to do.
To make a DC motor turn either direction, connect each wire to its own half bridge. Send half-bridge A HIGH and half-bridge B LOW to make the motor turn one direction, A LOW and B HIGH to make the motor turn the other direction.
To control the motor's speed, you turn the power on and off quickly, using a technique called "pulse-width modulation" or "PWM". Over the long term, a half-bridge that's HIGH 80% of the time and LOW the remaining 20% of the time gives the motor 80% as much power as one that's HIGH all the time.
The Motor Shield has all the hardware and software issues worked out, but like I said, even if you don't use the device itself, the circuit diagrams and the library code give you an example of stuff that's known to work.
When you void a product warranty, you give up your right to sue the manufacturer if something goes wrong and accept full responsibility for whatever happens next. And then you truly own the product.