If you want to modify your device, the first thing to do is to root it. You can then install many apps that require root privileges, as well as install TWRP and FireFireFire Bootloader.
I use the utility Breakdroid, and it is easier to use than KindleFireUtility, the Windows counterpart, because it does not require you to install any drivers, it just works. Here is the website. Go to downloads to download the Breakdroid tool for Kindle Fire.
http://northmendo.com/breakdroid/ Feel free to donate to the guy who made this.
1. Download Breakdroid and mount the DMG file.
2. Make a folder on your desktop or applications folder called 'Breakdroid' and copy over all the files.
3. Open the Breakdroid application. It will open a terminal window. Use option 5 'Kindle Fire Tools' and hit return.
4. An icon will bounce on your dock. It may bounce for up to a minute. It will then ask you if you want to open this application downloaded from the web. Click ok.
5. It will then show a dialog warning you that this voids your warranty. If you are attempting this, you should know this already.
6. Now it opens another terminal window.
7. Type '1' and press enter. Follow prompts. Make sure you follow any instructions exactly. Follow all the steps until step 8. You can use step 9 to donate to the guy who made this. It is optional.
8. Finally you can use step 10 to quit the Kindle Fire tools.
9. FireFireFire has been installed as bootloader and you have rooted your device.
You can use TWRP which has been installed by the previous guide to install ROMS, backup the current system and recover from any problems.
1. To access the TWRP recovery, shut down your kindle by holding down the power button until it shows a shut down dialog. Tap shut down.
2. Now turn the Fire on again. It will show a blue 'Kindle Fire' logo. This is the new FireFireFire bootloader which has been installed.
3. Keep your eye on the power button light. It should be green. Wait for it to flicker slightly. Or you can wait 2 seconds. Then press the power button again. It will show boot options.
4. Use the power button to cycle between the boot modes. Choose recovery to boot into recovery, then leave your Fire to boot.
5. Team Win logo will show, then the curtain will rise, showing a grid of buttons.
6. You have booted into recovery! Reboot without choosing recovery mode to get back to the normal system.
Install a ROM
1. Hook up your Fire with your Mac with a Micro-B USB cable. You can get them cheap on eBay, but mine broke after a few weeks, so feel free to find a more reliable vendor.
2. Download a ROM for your Fire. I'd recommend the GedeROM if you want an Ice Cream Sandwich ROM, or MoDaCo if you want a modified stock ROM with Google Play Store preinstalled.
3. Copy over the .zip file, placing on the Fire which has mounted on your desktop. Also copy over the gapps .zip if provided if you want the Google Apps package.
4. Eject the Fire and disconnect it from the Mac.
5. Use the previous guide to boot into Recovery.
6. Tap the Backup button and backup your system. This is very important, especially when installing your first ROM.
7. BACKUP YOUR CURRENT SYSTEM! For good measure.
8. Now tap the home button at the top right of the screen. Now tap Wipe, then tap Factory Reset. Then wipe Cache, then wipe Davlik Cache. Finally System Wipe. (Thanks to Thepooch for the best way to do this bit!)
9. This will wipe the device, so make sure you've Backed up your Fire! (See steps 6 and 7).
10. Now go back to the home screen using the home button and tap the install button.
11. Choose the ROM .zip file which you placed on the sdcard. I hope you named it something easy to remember and identify.
12. Tap install.
13. If it fails, restore from the backup you made (see how important backing up before wiping is?) and make sure your ROM you downloaded was downloaded properly. Also make sure it's the original zip file, not expanded or recompressed. Then repeat. If all else fails, try a different ROM or just stay with stock.
14. If it was successful, then go back to the home screen, and if you downloaded a gapps zip file, flash this as well, in the same manner as the ROM zip.
15. Reboot into system using the reboot button on the home screen.
16. Successful? If you don't like your ROM, you can always revert to stock using your backup, or install a new ROM following these steps.
If you found this guide helpful, please click the Thanks button. It means a lot.