Amazon has posted an official guide to access and test the Alexa Voice Service using a Java client (running on a Raspberry Pi) and a Node.js server on GitHub.

Amazon Tap is a portable Bluetooth and Wi-Fi enabled speaker that gives you rich, full-range sound. Just  by tapping on the microphone button you can ask for music, hear news, search for information, order a pizza, and more with the Alexa Voice Service.

Unfortunately, due to limitations with Amazon's Voice Services, the catch here is that your DIY build won't listen for trigger words like Echo and Echo Dot. Instead, you'll have to hit a button to issue commands.

To get started with this build you'll need a Raspberry Pi 2/3 and an USB microphone as Raspberry Pi does not have a built-in microphone.

For the complete detailed steps follow the instructions posted at Github.