SQUINTING MODIFIERS
It's appropriate that problems with modifiers have the most delightful names. A "squinting modifier" is one that seems to be trying to modify two things at the same time. (It can't quite see its way to do its job properly.)
Students who hand in their papers late often get lower grades. Do we mean that this is something that happens to students who are frequently tardy with their papers or that such students are often penalized? Placing the often before the verb hand in solves the problem (if that's what we mean).
Students who pay attention in class most of the time get higher grades. Putting the modifying phrase at the end of the sentence (or at the beginning) will solve the problem.
DANGLING MODIFIERS
Remember that when we begin a sentence with a modifying word or phrase, we must make sure the next thing that comes along can, in fact, be modified by that modifier! (That is, don't let that modifier dangle!)
By changing the oil every 3,000 miles, the car seemed to run better. (The car didn't change the oil. Whatever follows that initial phrase has to be someone that can change the oil.)
By changing the oil every 3,000 miles, Fred found he could get much better gas mileage.