In Time Clauses:

While I was coming to class this morning, I witnessed an accident.
While coming to class this morning, I witnessed an accident.
Coming to class this morning, I witnessed an accident.

When she opened the box, Jocelyn gasped at the sight of the diamond ring.
When opening the box, Jocelyn gasped at the sight of the diamond ring.
Opening the box, Jocelyn gasped at the sight of the diamond ring.

Before he left the house, Mr. Russo remembered to turn off the oven.

Before leaving the house, Mr. Russo remembered to turn off the oven.

*Make sure the subject of the main clause and the subject of the participial phrase are the same.

While taking a shower, my sister called from California. (INCORRECT)
While I was taking a shower, my sister called from California.
While taking a shower, I received a call from my sister in California.


In Absolutes:

The vase was knocked over by the cat. It lay in a hundred pieces on the floor.
Knocked over by the cat, the vase lay in a hundred pieces on the floor.

The mouse snatched up the larger pieces, and it left the crumbs for the cockroaches.
The mouse snatched up the larger pieces, leaving the crumbs for the cockroaches.

The little boy was lost and afraid. He called for his mother.
The little boy, lost and afraid, called for his mother.
Lost and afraid, the little boy called for his mother.