The first riot shield is found in the "Prison Break" mission, you'll be attacked by several enemies wielding them after you've broken Alejandro out of his cell.
There is also riot shield enemies in the "Ghost Team" mission (where you're attacking the base where Graves is holed up in) and in the "Countdown" mission.
To kill enemies once you've picked up the riot shield, simply get within melee distance and press the "shoot" button.