The OverDrive App is now available for Android products! You can download it free of charge through Google Play, the new Android Marketplace, on your smartphone or tablet.
An exception to this rule is with the Kindle Fire. The App Store on the Fire is run through the Amazon marketplace, which is a subset of the Android marketplace that, unfortunately, does not at present carry the OverDrive App. However, there is a fairly simple way around this.
Amazon's default settings of the Kindle Fire make it so that you cannot download third-party (i.e. non-Amazon) apps. To their credit, they make it fairly easy to turn this setting off. The first step in getting the OverDrive app to your Kindle Fire is to tap the gear at the top of your screen to go into the device's settings. Next, select the far right option that reads "More..." Scroll down and tap where it says "Device". Towards the bottom of the screen, tap where it says "Allow Installation of Applications From Unknown Sources". Naturally, a warning about the security of your Kindle pops up. Select OK. You should now be allowed to install third-party applications to your Fire.
The next step is to open the web browser on your device and to head to Overdrive.com.