The VNH5019 requires four digital and two PWM signals, and is compatible with 3.3V and 5V signal, so as long as your TM4C123G LaunchPad controller can supply those signals the VNH5019 shield should be fine.
You can wire both of the motors for a side in parallel to control each side from one motor output.
You can see the connections needed for use as a general purpose driver (including the motor power connections), in the “Dual VNH5019 motor driver shield connected to a microcontroller” diagram in the “Overview” section of the VNH5019 shield’s product page. The “Board Connections” section of the “Pololu Dual VNH5019 Motor Driver Shield User’s Guide” has a pinout chart describing how the MxINA and MxINB signals control the motors direction.
We do not have any example code for the TM4C123G LaunchPad, but you might take a look at the link to the library labeled “library’s github page” in the “Programming Your Arduino” section of the same user’s guide to see how you might go about controlling the driver.