I am looking to write an app that receives pushed alerts from a server. I found a couple of methods to do this.
I recommend using GCM - Google Cloud Messaging for Android It's free, and for simple uses it's should be very easy.
However it requires to maintain a 3rd side server to send the notifications on your behalf. If you want to avoid that there are some very good industrial solutions for Android push notifications service:
Diclaimer - I work in PushApps and also use their product in my applications for over a year now.