Daphne's link is a good suggestion and well worth reading. But the easiest way to get an Android application on a PlayBook is to download it from BlackBerry World. Unfortunately it can be difficult to tell before hand if an application is an native PlayBook or an Adroid application. A good example is Pool Break Lite by Kinetic Bytes.
If someone has taken an Andoroid Application and converted it to a PlayBook application but for some reason hasn't put it up on BlackBerry World (likely because they aren't the application vendor, sketchyness of this varies) then you would use the proceedure Daphne linked to. A good example of this is the Kindle Reader by Amazon. The application is free, and Amazon benefits from people installing it on PlayBooks and buying book from them, but they haven't made an official PlayBook application.
If no one has done either of these things then it is a bit more complex, and may even be against the law, depending on where you are.
Finally not all Android applications can be converted into PlayBook applications.
If there is an Android application you would like to run on your PlayBook, contact the vendor and let them know. RIM as been aggressively courting Android application vendors so there is lots of help and incentive programs. Have all your friends with PlayBooks do the same.
My other Blackberry is a PlayBook.