Adobe decided to kill off support for its Flash Player on Android a while back. Unfortunately, that didn't mean all Web sites you visit would start using HTML5 instead of Flash (though it would have been nice). So what can you do if some of the Web sites you want to look at are using Flash and your new Android device doesn't have support for it?
Fortunately, the last version of Adobe Flash Player that landed on the Google Play Store will work with your Jelly Bean device. However, since it's no longer available through the Play Store, you'll need to install it from a side-loaded APK. This means that someone exported their copy of Flash Player and uploaded it so you could install it manually.
You'll want to check if side-loaded apps can be installed on your Android Jelly Bean device. To do this, simply open the Settings menu, then go to Security and make sure that Unknown Sources is enabled. You may see a warning about third-party software, which you will need to accept in order to continue.
Installing Adobe Flash Player
Disclaimer: Installing third-party software means taking risks with your device and/or personal information. You will be responsible for any issues caused by the installation, and should only proceed if you are prepared to deal with these possible consequences.
Luckily, one of the helpful people on XDA-Developers created a thread dedicated to Adobe Flash Player for Android. The most recent download link can be found here: http://d-h.st/x4v, which should be accessed by your Android so it can be installed quickly. If you'd like to download to your computer first and then move it to your Android's storage later, that's fine too.
Now that Adobe Flash Player is installed on your device again, you'll need to use a mobile Web browser that still supports it. Right now your most stable choices are Mozilla Firefox and Dolphin Browser. You don't have to use the browser you pick for every Web experience on your device. Instead, you could just opt to open them for the Web sites that still rely heavily on Adobe Flash Player.
Now you can continue enjoying those Web sites that are stubbornly sticking with Flash.
Have you considered not visiting a Web site anymore because it hasn't converted to HTML5? Share your experiences in the comments.