Instructions
Look on the bottom of the Sony PSP console. You will see a white sticker with a barcode and a model number. The model number will read "PSP-1001" if you have a North American, "fat" model PSP. Japanese models (sold only in Japan) will have "PSP-1000" as the model number. Having a "fat" model PSP will mean that you also have the "fat" PSP battery.
Remove the battery cover from the back of the console by pressing in on the tab that is marked "Push." This will release the battery cover and allow you access to the battery.
Remove the battery from the PSP and look at the sticker on the battery itself. A fat battery will be identified by the product number "1800mAh."