While on the Amazon.com homepage, search the following keywords "Amazon Appstore" in the search bar under the header of the website. Once on the search results page, you see the first two links are similar, the first one is for tablets, while the other is for most supported devices.
You may need to confirm that your device allows the installation of the Amazon Appstore before you can access it. In order to allow the installation of the Amazon Appstore, you have to go to the Settings option on your device. Once there you have to access the Applications or Security section and locate the Unknown sources option. If the option for Unknown sources is not checked, simply tap the check box and then tap again to confirm.
Once you have allowed for your device to install the Amazon Appstore, you must find the correct Amazon Appstore in the Amazon Marketplace. If you were to search for "Amazon Appstore" in the Amazon Marketplace, the first two options would more than likely be what you're looking for. The first option is for tablet computers, and the second option is for most app-supported devices; choose whichever one best suits your needs.
After you have downloaded the Amazon Appstore from the Amazon Marketplace, all that is left to do is run the installation process. To do this, open your notifications after you have finished downloading the Amazon Appstore, and tap the file named "AmazonApps-release.apk" Once prompted, tap Install, tap Open, then sign into your Amazon.com account.