Watch the Billy Gibbons online guitar lesson by Jeff McErlain from Kings of Tone
A great way to use an overdrive pedal is to push the front end of an amplifier that is already distorting a bit. By turning the volume up on the pedal it functions as a boost in volume that drives the tone stack of the amp thus producing more gain. I dial in the amount of drive on the pedal to taste, it may be different for each guitar, amp, or tune. I remember buying my first Tube Screamer and plugging it into my clean amp and thinking "This doesn't sound like Stevie Ray!". I had no idea that he was using the pedal as a boost, not the sole provider of the overdrive. There are countless OD pedals available, but if you are on a budget, the classic Ibanez Tube Screamer is an excellent choice.