Watch the Keith Richards online guitar lesson by Jeff McErlain from Kings of Tone
Keith's lightly distorted tone is fairly easy to emulate with a good overdrive pedal. Fortunately there are many inexpensive overdrive pedals out there to choose from. I always look for one that interacts well with my guitar's volume knob. When I turn down the volume the pedal should clean up accordingly just like a good amp. Each pedal is different and each pedal has a sweet spot for each amp, so experiment! I have many OD pedals, too many in fact! Don't go crazy here, I can recommend the Bad Monkey pedal by Digitech as an excellent inexpensive overdrive.