With OS 10.2.1 BlackBerry will be bringing the ability to install Android APK files right on the device from the Browser or File Manager. Unlike previous OS versions where you had a lengthy process of converting the APK to a readable BAR file, then sideloading using any number of methods, you now are just a few taps away from getting a plethora of Android apps on your device quickly and easily.
Keep in mind that this is only for OS 10.2.1.1055, so if you're not running the leaked OS (or a higher version we'd imagine) then this won't work at all.
As of now there are a few ways to download APK files to your device, all of which are fairly easy.
Grab an APK from the CrackBerry forums
Many members have already posted up some threads like this one with working APK files. All you need to do is download the APK to your device memory or media card, then tap it to install.
Use the APK Downloader
For access to more specific APK files that you may want you can use the APK Downloader here. You'll just need the Google Play URL of whatever app you're looking to grab. Download it, tap to install and you're good to go.
Install a third-party app store
Perhaps the easiest way to find Android apps is with the use of a third-party app store like Amazon or 1Mobile. Just head to the respective link, install the app store APK and browse away. These app stores have loads of popular free apps and making finding what you want a breeze.
If downloading a file from your device, when it's complete just tap the file in the downloads view and then tap install to begin. If you're transferring the APK files to your device, use the File Manager to locate the APK then tap it to open and tap Install to begin.