I didn't notice Patrick's edits before but I should correct one or two things in it:
EDIT: It's unknown the exact mechanism through which DOMS occurs.
Most of the mechanisms of muscle soreness and DOMS are very well understood, the parts that still need more study are interesting academically but don't have too many practical implications.
I am saying this because people should -not- get the wrong impression that, ~hey we don't know anything about it so anything is possible~.
Specifically, we do know it's a good and necessary thing for substantial muscle growth. We have some uncertainty about what are the major factors in turning on this growth mechanism and are still sorting out some side details. For example some evidence shows it's not always caused by microtrauma, but then again microtrauma will definitely cause it, and who cares exactly if there are even 10 ways to get there.
It's also not too hard to tell good soreness (starting 24hr after, peaking at 48hrs after, and then lasting 2-4 additional days) apart from soreness in overtraining, or other things that might feel similar but don't have all the nice associated muscle growth mechanism with it and are caused by other things.
Chocolate milk is a good recovery food, but I don't know that it will keep you from being sore.
Since the soreness you feel from muscles growing is a good thing, no healthy food will reduce it (poison and starvation might shorten it but for all the wrong reasons)
From what I understand, it's okay to train through DOMS, though if you're constantly sore over several days, you may be overtraining. ...
As far as training while sore, you can definitely do it, but you don't always want to, depending on what you are trying to improe with your training.
If you could only work out twice within a week, you would be better off spreading them out so you can recover as much as possible before your next workout.
To think that working out while your muscles are trying to grow has no effect on your total growth would be naive in my opinion, and even in terms of your max muscle output we know it is reduced, so that second overlapping workout won't be as good as it could be.
But, if you can workout as often as you like, squeezing an extra workout even while sore would still end up giving you better total results than skipping it, as long as it doesn't cause you to become overtrained. Just think of each workout while not sore as being say 100 points, and ones while sore as being like 50 points or something.
And different things recover at different rates, muscle size vs strenght vs coordination, so you can always try to plan overlapping workouts to focus on more different aspects (e.g., maybe some techniques would lead to injury if you are still sore so you can train them on a different day to be safer, etc).