1. The newspaper reporters were hot on the trail of a good news story. The man they were pursuing didn’t want to be caught, so he tried to mislead them by throwing them a red herring.
2. The elected officials in congress don’t want the voting public to concentrate on the issue of higher taxes. They divert the public’s attention by constantly raising another, less important issue that is nothing more than a red herring

The expression originates from the fact that a red (smoked) herring has a powerful and persistent odor. Centuries ago red herring was used to train dogs to track scents. Those hoping to misdirect tracking dogs would drag red herring across their trails since a dog that gets a whiff of red herring will lose any other scent that it has been following. This expression is often used in the context of mystery stories.