This article is from http://forums.crackberry.com/blackberry-playbook-f222/27-steps-android-apps-your-playbook-631759/ and is on here for posterity sake (didn't want to lose the steps)
Just shortened this to steps.
OK here is my best to make a guide for installing Android apps.
1st off credit goes to the folks over at n4bb.com for the Android Player leak, and info oninstalling apps.
Also to louis.keeper for his how to on side loading
Also credit to offthahorseceo for the method of loading apps from within the file manager.
Thanks to HataX and TerrenceRowl for simplifying the process.
And note for admins/mods: Remove any offending links as required 
1. Enable Development Mode on Playbook (Settings/Security/Development Mode then set to on)
Note the development mode icon indicator, press it and note the IP address (we'll use 192.168.1.131 for purposes of this howto)2. Download sys.android.bar file
3. Side load the Android Player (see link here on general side loading)
4. Download and install platform-tools
5. Unzip into "C:\"
6. Run Android Player on Playbook.
7. When loaded swipe down from the Top of the Playbook
8. Click Set Home view and select Installed Applications. Hint: To navigate backwards, swipe left from the bottom bezel on the Playbook.
9. Select Settings/Applications and check the Unknown sources box.
10. You must now close Android Player and Reopen it (Leave the Android Player running!)
11. This is also a good time to dowlonad some apk files. The first one you will need is Astro file manager
12. Move the file downloaded in step 6 into the "C:\platform-tools\"
13. Hit the start key and in the search box type cmd and hit enter.
14. Type: "cd C:\platform-tools\"
15. Type: "adb connect 192.168.1.131:5555" Replace with your ip
Screen will read: "connected to 192.168.1.131:5555"16. Type "adb root"
Screen will read: "restarting adbd as root"17. Type "adb connect 192.168.1.131:5555" Replace with your ip
Screen will read: "connected to 192.168.1.131:5555"18. Type adb install Astro.v2.3.1.noexpire.apk
Screen will eventually read: "Success"19. Take a deep breath the hard part is now over.
(Dont worry, Steps 14-19 are only for the installation of the file manager)
20. Find the desired apk for the program you want to install. copy it over to the playbook using the USB cable or WiFi connection, put it in the downloads folder.
21. Navigate back to the apps page
22. At the bottom of the list you will find ASTRO, run it.
23. Navigate to the Download folder and click the app you want to install.
24. Select the "Open App Manger" Option
25. Select "Install" and "Install" again
26. Select "Open" and there you go...26 steps to installing android apps on the Blackberry Playbook :-)
Programs needed:
Platform-tools
JRE 32 Bit or 64 Bit
DDPB Installer
sys.android.bar file
ASTRO