Being able to access the Google Play store with your FIre HD involves more than installing the Dolphin browser. I believe you would have to root your Fire to access the Google Play store.
To install the Dolphin browser, you can go to someplace like 1mobile.com and install it. You'll have to sideload it; first go to Settings > More > Device > Allow Installation of Applications On/Off and turn it on.
Then, go to 1Mobile and download the Market, then download the browser. Once the notification indicates that the download is complete, tap on the notification to install.
A forum community dedicated to Amazon Kindle owners, authors, and enthusiasts. Come join the discussion about publishing, audio, troubleshooting, models, styles, reviews, accessories, classifieds, and more!