Dangling participles occur where the first part of the sentence and the clause that follows just dont belong together, and therefore dont make sense.
Driving through Taranaki, Mt Egmont dominates the landscape. Mt Egmont (now more usually called Mt Taranaki) definitely does dominate the landscape of Taranaki; but it most certainly cant drive!
Crossing the room, her foot bled all over the carpet. Ever seen a foot cross the room all on its own?
Driving home in yesterdays storm, a tree fell on the back of my car. Once again, we have a distinctly strange driver at the wheel.
Then there are those sentences where characters are doing several things at once that just arent possible:
Bending down, she laced up her shoes, grabbed her keys from the table and raced from the room and down the stairs. Thats an amazing number of things to be able to do while bending down! Think about it. Possible rewrite: She bent down, laced up her shoes, grabbed her keys from the table and raced from the room and down the stairs.
Slamming the car door, he locked it and hurried inside the house. This is not quite as exaggerated as the first sentence, but the fact remains that nobody can lock a car door, let alone hurry into a house, while still closing the car door. Possible rewrite: He slammed the car door, locked it and hurried into the house.
Id also like to point out that detailing every move your character makes (as Ive done in these examples) is boring. Dont do it too often. Preferably do it only when such actions turn out to be more important than they seem.
The above examples all use present participles, but you need to beware of dangling past participles too:
If properly installed, you shouldnt be able to open the door without first pressing the safety button. Possible rewrite: If the (whatever item is actually being installed; you certainly aren't) is properly installed, you shouldnt be able to open the door without first pressing the safety button.
In evening clothes and with her hair specially styled, Mark always thought his mother as glamorous as a film-star. It pains me to admit it, but this example came from my own writing and it was many months before I noticed it and rewrote it to read: In evening clothes and with her hair specially styled, his mother had always seemed to Mark as glamorous as a film-star.
Relieved, although half-naked, Mom handed me the catalog. This would be okay if it was actually Mom who was half-naked, but it was (of course) the narrator, and the image this sentence created startled me right out of the story.
Since hanging or dangling participles usually start with words that end in -ing, go through your manuscript looking for such words and change any offending sentences. Dangling past participles are harder to find, so I hope the above three examples will help you recognise them.