Well you could buy a pedal like a Boss -DS2 or if your amp has an overdrive button you could flick that on. If you have a tube amp you could drive up the volume or gain until it breaks.
My amp has a setting called drive but thats not the same thing right?
Go out and get yourself a boss distortion pedal. Its 40$ and is perfect for beginners. Its an orange pedal that says Distortion on it. Very plain and simple, yet still a great pedal that can be used forever.
i reccomend the Electro Harmonix Metal Muff over the boss ds 1 distortion it can do everything from light overdrive to full on metal distortion. plus its cheaper i think. and boss' break easy