Question: I want to know what are the requierements to implements Push Notifications in an android and iOS app. 

I have a hosting plan to host my website and PHP scripts, so my real question would be if push notifications are made by php scripts or by a program that would need to be installed into a dedicated server.

Thanks in advance

Answer: 
Generally, `Push Notifications` are sent not directly by you, but by servers hosted at Google / Apple. 

On your server, you make a request to these servers in order to get your push notification delivered. These requests can be set up using various web programming languages, e.g. Java/PHP/Python/...
There are already open source libraries that will come in handy for you, e.g. [APNS-PHP](https://code.google.com/p/apns-php/) (iOS). For sending notifications using `Google Cloud Messaging` (Android) and `PHP`, see this [SO post](https://stackoverflow.com/questions/11242743/gcm-with-php-google-cloud-messaging).

For general introductions, see

* [Local and Push Notification Programming Guide](http://developer.apple.com/library/mac/#documentation/NetworkingInternet/Conceptual/RemoteNotificationsPG/ApplePushService/ApplePushService.html) (iOS)
* [Google Cloud Messaging for Android](http://developer.android.com/google/gcm/index.html) (Android)
There's another services less expensive like [Pushwoosh](http://www.pushwoosh.com/), [Mainline](http://www.mainline.fr/) , even Parse can do it.