You can also do a quick search on how to use MQTT with android, one is the Paho Android Services (I never personally used that one before) you can read more about it here Paho Android Service - MQTT Client Library Encyclopedia.
There are also other Android MQTT services you can leverage. So one path I would recommend
- Spin up a Soalce broker (as per the quick starts that Tom referred to)
- Use MQTT Android to connect to the broker
- Send and receive messages from your Android application over the broker
Using the Java API from our downloads page will give you more advanced features access, the reason why I suggested MQTT at first is to get familiar with our broker and pubsub workflow. I’m curious to know how your Android application turns out to be and what it is! Would be happy if you update us on it and the progress 
Happy programming!