Watch the Beer Drinkin' online guitar lesson by Jeff McErlain from Play in the Style of Billy Gibbons
If you want to get a similar tone to Billy's it can be done with some pedals into a clean amp. There are so many overdrive options out there that it is staggering and somewhat overwhelming. What I suggest you look for is one that cleans up well when you roll your volume knob back and reacts to your pick dynamics. These are hallmarks of a good amp and therefore a good pedal! Unfortunately not all amps play well with all pedals so it may take a little investigating. When a student asks me what OD pedal to buy I almost always suggest the Fulltone OCD. I am not endorsed by Fulltone so I'm not trying to sell you something! It is my experience that that pedal sounds excellent into many different amps and is very hard to get a bad sound out of. It is also very reactive you dynamics and volume knob changes. I think it's a good choice if you want a good OD pedal. Others I like are the Z-Vex Box of Rock and the Blue Note OD by Rockett Pedals. None of these pedals are inexpensive, but it may become your most used pedal, so don't skimp if you can avoid it!