Here are a couple videos on youtube that might help you understand:
During the plays there are the "chanters" who voice the characters and narrate. Most shows only have a couple, but the first one we saw had 5 of the chanters and 3 shamisen players, which made it really dramatic. The puppets are typically operated by 3 people, and in most schools of bunraku only the lead puppeteer is allowed to reveal himself; the rest are hidden in black costumes. The lead puppeteer operates the head and right arm, the 2nd puppeteer operates the left arm, and the lowest level puppeteer operates the legs/bottom/body.
The downside to bunraku (even for many native Japanese speakers!) is that it developed in Osaka a LONG time ago. What this means is that the plays are performed in the Osaka dialect. This in and of itself is a problem, because the average person who isn't from Osasa/Kansai area doesn't particularly understand that dialect. Then top it off with the fact that it's an archaic version of this dialect from the 1600s, and it becomes nigh impossible for people speaking standard Japanese to understand. During the play it was subtitled in the standard Tokyo dialect along the sides of the stage, which I found to be pretty amusing :) It kinda sucked not being able to understand what was being said (though I derived a bit of comfort from the fact the Japanese people didn't understand the speaking either) but you can infer quite a bit from the tone of the chanter's voices, the music of the shamisen, and the puppets themselves.