Sarina DuPont from Embarcadero has a blog post up with a write up on how to setup push notifications using the new Delphi XE6 Firemonkey components. Her tutorial uses the TKinveyProvider and and the Kinvey web service to handle sending the push notifications. What I like about the Delphi XE6 push notifications is how seamlessly they integrate the Android GCM and the IOS APN implementations into the same components. The tutorial only covers setting up the GCM keys however. Sending push notifications is a somewhat complex process to set up as you have to get all of the right keys and IDs for Android GCM and IOS APN and plug them in correctly in addition to having the right permissions set on the client applications. The TPushEvents component that is used in the tutorial has a couple properties that make it easier which are the AutoActivate property and the AutoRegisterDevice property. Once you have it all setup you actually send the push notification itself from the Kinvey website. The push notification components use OpenSSL so for them to work on IOS you need to include the OpenSSL static library in your deployment but Android ships with OpenSSL already.
Head over and read the full tutorial about setting up and sending push notifications with Delphi XE6.