Clarity is one of the keys to effective writing. Confuse the reader once and she glances over at the television set, the XBox, the iPod, or the romantic interest. Confuse the reader two or three times and you might want to reconsider your future career as a the next Dan Brown or J.K. Rowling.
Stray clauses are one of the killers of awkward prose, and I've always preached that if you can function competently at the sentence level, all the rest can be learned through study and practice. We'll get to comma usage later, but for today, let's take a look at descriptive clauses.
I recently edited a manuscript sample that contained a sentence "He killed his wife and children as they were asleep in their beds with a shotgun." I can't be sure, but I assume the killer used a shotgun, not that the warm-and-fuzzy family cuddled up with shotguns and teddy bears at night. The sentence could be made clearer either by shifting the descriptive clause closer to the "acting agent" (the man who used the shotgun) or totally restructuring the sentence.
One possibility is "With a shotgun, he killed his wife and children as they slept." Simple and effective, though not very artful. Personally, I would build a little suspense and use a series of short sentences--"The shotgun was cold in his hands, but warmth radiated from his sleeping wife..."
My first draft of a newspaper story I wrote this morning contained the sentence "Watauga County Republican Party chairwoman Pam Blume encouraged her fellow party members to work hard during Saturday's meeting..." I immediately caught the error, because she wasn't asking conventioneers to work hard just for that hour on Saturday, she wanted them to work hard during the entire election year. I moved the clause to the beginning of the sentence and ended up with "During Saturday's convention, Watauga County Republican Party chairwoman Pam Blume encouraged her fellow party members to work hard in the election year."
The basic lesson is to place the supporting or related clause as close the the subject as possible. An ancillary lesson, learned through years of mistakes and revisions, is simply to not write anything you have to revise later. Leave out the bad parts. Write good.