Don't share or retweet until you've (a) read the story and (b) checked it out.
Check other news sources and fact-checking sites to verify information presented in news stories.
Content and photos posted on social networks can contain invisible but important data that will help you determine whether they are being used deceptively.
First Draft News, a nonprofit organization that is "dedicated to improving skills and standards in the reporting and sharing of information that emerges online," maintains a fantastic list of techniques for verifying everything from the oldest known version of an online photo, to the upload time of an Instagram post, to whether a social media account actually belongs to who it says it does.