Searching for and verifying military awards for valor has always been a labor intensive process requiring requestors to submit a Standard Form 180 request to the National Personnel Records Center. While this remains the best way to verify awards, a couple of other options are available for researchers.
In the wake of the Supreme Court decision invalidating the Stolen Valor Act (which made it illegal to lie about your military awards), the Department of Defense announced that it would create its own, searchable database of military valor awards. The DoD site contains a searchable (but not quite complete) list of awards made after September 11, 2011.
Also, check the Military Times Hall of Valor which contains records of over 140,000 awards of valor. As with the DoD site, absence of a record of an award on this site does not necessarily mean the award was never made.
Finally, lots to know in this world with lots of complexity to the language. So, get a translator -- someone who knows that they add "oak leaf clusters" to Purple Hearts to indicate the recipient received multiples of the award, for instance. Otherwise, you run the risk of being wrong in your claim that someone else is making a false claim.