Instructions
Check for a price difference between the PSP and other models in the store. If the PSP is significantly less expensive, it could be a refurbished model. Most gaming stores and online retailers sell refurbished devices at a discount.
Look on the packaging. It will display "Refurbished" if the product is used.
Look in the fine print of the product if you are purchasing it online. Websites such as eBay and Overstock sell refurbished items, but often list the information in the fine print. Read through all of the information, and if there is no mention of the device being refurbished, it is a new product.
Look at the website you are buying the product from. Unless it is an officially marked Sony retail store the product is refurbished.