I recently bought a Kindle Fire because they are great value for an Android tablet and I knew they were ways of installing Google Play so I could access the apps I had already purchased through Google Play without having to repurchase them from Amazon. Specifically I wanted Minecraft for my son to play - honestly, for my son ;-)
The Fire I bought was the 5th Gen Kindle Fire (not HD, I wanted inexpensive!) and the awesome instructions on How To Geek worked perfectly at installing Google Play. I highly recommend this solution for installing it, it was simple to follow and easy to do. From here I was able to log in to Google Play and download my apps including Minecraft which I had previously paid for on another device
If all you want from this is to install apps from Google Play using your account, you are all set! However, if, like me, you also want to add a second Google user (in my case, my son) so he can use his account to synchronise his games, I got a bit stuck. Unlike an Android tablet, there is no 'Accounts' option in the settings to add new Google accounts. The installation above does install the Google Accounts app, which is used to store account details, but there doesn't seem to be a way to access it directly. Google Play also doesn't have the option to add a 2nd account and relies on those already added
The solution, it turns out, is really simple. Simply install another Google app that requires an account (such as GMail). When you start the app, it will ask you to associate it with a Google account.
You can now add a different account and it will get added to your accounts on your Fire. You can verify this by opening Google Play and you should see that both accounts are now selectable. So if, like me, you want to use your own account but also want someone to be able to use their account for synchronising games, you can :)