What are examples of sentences and sentence fragments?

A sentence makes a complete thought. A sentence fragment does not.

Fragments :
The coach who had arrived for the big game.
Can get in the way of people trying to work.
Turning to the left at the old mill.

Sentences:
The coach had arrived for the big game.
Pedestrians can get in the way of people trying to work.
Turn to the left at the old mill.
The road will be turning to the left at the old mill.


Making fragments into sentences:
Example:
The excited crowd watching the game. (fragment, no predicate)
After a brief intermission during the game. (fragment, this is a prepositional phrase)

After a brief intermission during the game, the coach sent in his star player, drawing cheers from the excited crowd watching the game. (sentence)

Example:
Help finding the cat. (fragment)
The boy's mother standing in the living room. (fragment)

He saw the boy's mother standing in the living room, telling her son that she needed help finding the cat. (sentence)