Delayed by about a month, BBM for iOS and BBM for Android both have been listed in their respective app stores. BlackBerry also has come up with another way to receive the app which requires you to head over to BBM.com using the browser on your phone, leaving your email address, and "waiting in line" to start using the messaging app. Those who previously registered with BBM.com should be able to use it immediately.
And if you need help running BBM on your iOS or Android phone, you can check out the videos below. One of them just might have the answer that you're looking for.