There is currently no way to display a webp image on any native app on an Android device, including the web browser. You will have to look into 3rd party apps to display these images.
According to the WebP mailing list, they are working on incorporating WebP support into the Android SDK. They did not say when exactly they plan to release this but when they do you should be able to save bitmaps as WebP format as well as JPEG and PNG.
EDIT: Android 4.0 aka Ice Cream Sandwich now comes with native support for the WebP format. You can see supported file types at the Android developer site.
