Kindle Fire comes only with the tiny Amazon marketplace, Installing the full android market on the kindle fire was probably not an option for amazon as they needed the monopoly on the apps sales in order to be able to offer the Kindle Fire at the light price of 199.
Luckily, installing the Google Market place on the kindle fire is now an easy task. All you need to do is to root your kindle fire and copy the market apk to the system apps folder manually or using the kindle Fire utility.
How to install Android market on Kindle Fire?
Well you have two options, Rooting is required for both:
1. Use the Kindle Fire utility By the elites at XDA developer: This is the Easy way. download the KFU, start it, then select Extra(6) then install Google apps & Go launcher EX (2)
2. Download the vending apk, extract it then copy the vending.apk to your Kindle Fire by usb then use your file explorer to copy it to /system/app. then reboot. once done install the market opener apk to show the market icon nicely in the kindle fire’s apps view.