Introductory verbal modifiers are introductory phrases that naturally adhere to the subject of the main clause. When the subject of the main clause is not the performer of the action in the phrase, a dangling modifier is the result.
Wrong:
Patting her curls, the afternoon stretched long and hot before her. (She, not the afternoon, was patting her curls)
Correct:
Patting her curls, she watched the after stretch long and hot before her.
As she was patting her curls, the afternoon stretched long and hot before her.
Wrong:
While dreaming of dancing sugar plums, the children's nap continued through the dreary afternoon. (Who is dreaming, the nap or the children?)
Correct:
While dreaming of dancing sugar plums, the children napped continuously through the dreary afternoon.
Wrong:
Snuggled up near the crackling fire, the winter storm raged while the children read a book. (The children, not the storm, are snuggled up near the fire.)
Correct:
Snuggled up near the crackling fire, the children read a book while the winter storm raged.
Click on the link for some practice with modification.